Question
Polar of origin (0, 0) w.r.t. the circle
touches the circle
, if
Hint:
In this question, we have to find the correct option if Polar of origin (0, 0) w. r. t. the circle
touches the circle
. As we know that the polar of equation is 0. So, using this and putting P (0,0), we can find a equation for perpendicular distance of a point P
and center (0,0) we can find the value of r and solving that we will get the correct option.
The correct answer is: ![c squared equals r squared open parentheses lambda squared plus mu squared close parentheses](data:image/png;base64,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)
Related Questions to study
Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s -1 The frequency of the incident light in s-1 is [h=6 x 10-34J-sec;charge on the electron=1.6x10-19C]
Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s -1 The frequency of the incident light in s-1 is [h=6 x 10-34J-sec;charge on the electron=1.6x10-19C]
Trajectories of two projectiles are shown in figure. Let
and
be the time periods and
and
their speeds of projection. Then
![](data:image/png;base64,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)
Trajectories of two projectiles are shown in figure. Let
and
be the time periods and
and
their speeds of projection. Then
![](data:image/png;base64,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)
A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and ![g equals 10 m s to the power of negative 2 end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAATCAYAAAD/PXGYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAjZJREFUeNrtWE9EQ3Ecf5JJMqbD7JBIskOHkXRMZJIkI0k6RYdO6TJJOnXpkExikh06RNIpu02SHWImHTp0yQ6TGZNMZh7r++UTz6/f2/a290/ehw/bd5v3/X3e9/v5ft8UxYPZaIB1YpY46kliPXqIW8S8J4V9qHkS2INp4oNbkhkj7hOfm3zHTzwjPoFJxJzyYhllCMGzR9wi9iVxs0nCjAxxUfN+ATE3g4voDoK7coLLsExMSOInxFWXCs0Cp9vpvn7iEbEMY78hnhLjDonN149K4jP4TIsD5BnEDSoRP4jz+DxAPCZWiF/EXeH3e8QCUUU+nZ6ZhQ63+lIvzDyO18wdXHypAx9rtLCHdsRmYXySuA9ianENwXOoes5/mPiOauOzrSA+hGIKaoQ+17mWGd7+BzyoDiXxNxu8R09stclv6pI8M6hgLYoQUhb/PRcPslk7vYZbblCymFcd9Gy1zf2V8/yGDSoG4trZkBcGsWWYID5K4lPE+w7XITNspKTT2n2CjejlaSQeggYcH7BS7BjWMBHsfSkHK5uH4JwkHhUGpF6eRuN8E1+I61YeltvnSmcP3nBQ7Bj8VkRKWP0S2NdFGI0zLohrVh7Wj7aM4H0ElVPEI6dTYito621sET5sDuIj8K1mxesmPkl8lcwuS6q7gCmfQ6uWMUzsfAQWEUC11TDUkhJPrcAClA7in7iuihsbVhzAuI61eOgSYfzZE9K0U9apu/zfMYChUUWrplHZHkzED0TMpIgckNyfAAAAoHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5nPC9taT48bW8+PTwvbW8+PG1uPjEwPC9tbj48bWk+bTwvbWk+PG1zdXA+PG1pPnM8L21pPjxtcm93Pjxtbz4tPC9tbz48bW4+MjwvbW4+PC9tcm93PjwvbXN1cD48L21hdGg+yh/8RQAAAABJRU5ErkJggg==)
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A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and ![g equals 10 m s to the power of negative 2 end exponent](data:image/png;base64,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)
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The equation of the circumcircle of the triangle formed by the lines
and y=0 is
The equation of the circumcircle of the triangle formed by the lines
and y=0 is
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown
![](data:image/png;base64,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)
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown
![](data:image/png;base64,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)
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to
![](data:image/png;base64,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)
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAACKCAYAAABrTuLXAAAgAElEQVR4nO29eVDUV7r//+oNegGafUdkBw0quOEGRpAEAxKJiUs0MZPEyUxmpnKrZjJz51Zyc+9kpiqVyczUneTeyUxu1tEYTaLEXaOAccWAQQ0gi4AoyNpNL9B0N92/P/Lr/gZB2bvbXF9VXVp0fz6f059+f855znOe5zkCq9Vq5R73+P8ROrsB93At7gniHoO4J4h7DOKeIO4xCLGzGzCVWCwW+vv7MZvNWCwWLBYLNhv6VltaIBAMeolEIiQSCe7u7s5outP4QQji+z/u9/+v1WopLS2lqakJrVZLX1+fXSADAwNYLBYEAgFCoRCRSISbmxvu7u7I5XL8/PxISkpizpw59vMKBAL7ub///x8Sgrt92qnVaqmtraWqqorW1lbq6uro6elBoVAQFhaGRCJBqVSiUCjw8PDA09MTpVKJj48PPj4+GAwGuru7UavVaDQadDoder0enU6HTqejr6+P5uZmAIKCgoiLiyM4OJikpCSio6Nxc3Nz8h2YXO4qQZhMJrq7u7l69SpNTU1UVVXR39+PQqEgJCSE++67z97ly+VyvLy8EIlEiMVixGIxIpHI/rL9zWKx2HsM27+2l9lsxmg00tPTg9FoRCAQ0Nvby+XLl+no6KC3txelUsns2bMJDQ0lIiKCgICAu7r3cHlBWK1Wbty4QVNTE42NjWi1WlQqFV5eXigUCqZNm0ZERARKpRI/Pz9EItGUtqevrw+VSoVaraa+vp729nb6+vrQ6XT2nigxMZFp06bh6+t71/UgLikI21PZ3t6OxWKhqKiIK1eu4OfnR05ODkFBQYSGhiKVSp3dVAA0Gg1tbW3U19dz4MABAGbPns2cOXNQKBT4+vo6RKyTgUsJwmg0YjQaaW9vZ8+ePZSUlJCYmEh6ejopKSmEhoY6u4mjorGxkerqao4dO0ZDQwNpaWk8/vjjeHp64u7ujkQicXYTb4tLCeL06dMUFhbS0tJCVlYWq1evRiqV2sd/ofDucJtYLBa7HdLd3c3hw4cpLCwkMTGRgoICFixY4Owm3hanC0KlUlFWVkZhYSFubm6sXLmSpKQklEolSqXyrjbQAMxmMzqdDrVaTWVlJUePHkUikZCdnU1mZqbLfT+nCaKnp4erV69y8OBBzGYzs2bNIjExkdDQUDw9PV3uRk0GPT09tLS0UF9fz7fffovJZGLlypUkJCTg7e3t7OYBThLElStXqK6u5sKFCwQEBJCdnU1UVBRi8Q/CTzYiBoOB1tZWdu/eTXd3NzNnzmTu3LmEhobi4eHh1LY5TBAmkwm9Xo9Go+FPf/oTHh4ebNy4kbi4OJc2sqYSq9VKZWUl27dvR6VSsWXLFqKiovDz83OaveQQQVgsFtrb29m+fTtHjx7lxRdfZMGCBSgUiqm+9F2ByWTi66+/5vPPP8disfDyyy/j6enpFFE4RBBfffUV+/fvJzg4mHXr1uHj44Obm9tdM2uYaqxWq90Le+jQIfbu3cu//Mu/kJqailwud2hbpkwQVqsVrVZLUVERx44dIycnh9TUVAIDA3+QBuNkYDab0Wg01NXV8c9//pPU1FTuv/9+IiMjHdaGKRFEf38/ra2t7Nu3j46ODnJycuxTyXuMjMlkory8nPPnz2M2m1m8eLHDfBeTLoi+vj6uX7/Op59+islk4oknniA8PPz/zAxiMmlububgwYPU1NSwYcMG7rvvvimPz5hUQfT399Pc3Mz7779PeHg4Gzdu/MH6FByFSqWiuLiYt99+m7/85S9ERUVNqSgmVRClpaUUFhaSnJzM2rVrEYlE98QwQaxWKwaDgcuXL/PKK6/w4osvkpGRMWXXmzRB7Nu3j6KiIrKysli8ePE9e2ESsVqtGI1GmpqaeOutt8jKyuKBBx6YkqX1Cc/7DAYDJSUlFBUVkZuby8KFC++JYZIRCAS4u7sTFRXFk08+yenTpzl+/PiUXGtCll5vby/Xrl1j7969rFy5kjlz5uDj4zNZbbvHLUgkEpKTkxkYGGDHjh2IRCLuv//+STXYx30mg8HA9evXef/990lLS2Px4sV4eXlNWsPuMTwSicQeePP73/+eoKAg4uPjJy1YaFw2hMVioaGhge3btxMXF8ejjz56V0QD/ZAwGo1UV1fzwgsv8Oc//5n77rtvUn6DcdkQLS0tfPbZZ/j7+5OXl3dPDE5AIpEQHx/PSy+9xFtvvcX58+cn5bzjEsTBgwexWq3k5+ffW6ByEjZDc8GCBSxcuJAzZ85w9erVCZ93TIIYGBhg//79XLlyxR7seg/nIRAIUCgUrFq1ColEwrFjx1CpVBM656gFYTQaqa+vZ8+ePWzcuJGEhIR7Q4WLEBISwpIlS2hoaODMmTMTOteoBGELFn3//fdJT09n+vTp/+dyHl2d5ORkVq1axfbt2+no6GBgYGBc5xmVIGw5kkKhkNWrV9/zNbggYrGYlJQUNm3axM9+9jN6enrGdZ5RCeLKlSvs2LGDp556CoVCcW99wkWRyWSkpKQQGxtLeXn5uEQxomPq+vXrlJWVkZ2dTWRk5A/KblCpVGg0GvR6PUajEZlMhlwux9vbG7lcftd9V6FQiLe3N48++iivvfaaPcVxLIwoiPLycrq6usjLy7trYxoaGhro7Oykra0NtVqNUCjEz8+Pnp4eNBoNvb29GI1GpFIpcrkcHx8fhEIher0ei8VCQEAAvr6+hISE4O/v7zIphMPh5uZGUlISCxYs4MyZM/j4+BAYGDjq4+/4C7e2tlJWVkZKSgoRERETbqyj0Gg09oRcNzc3Dhw4QE1NDSaTCU9PT2JiYoiPjycuLm5QRpjVarW/GhoaqKuro6GhAZ1Oh7u7O6mpqcyePdueWW4rN+BKCAQC3NzcKCgo4L//+7+JiorC19d31A/zbV3XFouFN954A39/fwoKCu6KFUyDwYDFYuHo0aN88MEHdHR0sHnzZhYtWkRoaChKpXJcvZzVaqW9vR2VSsXBgwfZuXMnQUFB/PnPfyYoKMhebcbVgoY//vhjrl27xtNPP42/v/+ojhlWEBaLhY6ODv7whz+wefNmUlNTXe7L3orJZOKVV16hpqaG9PR0li1bZp8eT0ZuqK0kkS2/5OrVq5w8eZLS0lJSUlLYuHGjy/WiHR0dfPTRR0ybNo21a9eO6phhBdHb28vbb7+Nj48PeXl5+Pn5TXpjJ4u6ujoOHTpEdXU1c+fOZeHChfj5+dlD/acCW8CKWq2mvb2dsrIy6uvrCQwM5LnnnnOZYcRsNnP48GFKSkr4j//4D2Qy2YjHiF555ZVXvv8Hi8WCVqvlgw8+YNOmTQQHB7tk79DV1UV5eTkff/wxSqWSrKws0tPTCQsLw9PTc0pnCAKBALFYjIeHB/7+/kRFRREcHExdXR0lJSX09/fj4eHh9LQ8oVCIm5sbVVVVGI1GoqOjR/wthwyoer2eM2fOMGPGDHx8fFxuZmEymWhsbOTs2bN88803pKWlkZWV5TRnmUgkwsfHBy8vL6ZPn86BAwcoLi6mpaWF9PR0oqKinNIuG0FBQWRlZfHZZ5+RlZU14oMyRC4dHR3s3r2b/Px8lwt4MRgM1NbW8sc//pH6+nqef/551q5d6xKeU5FIhK+vL5s2beL555+nqqqKN998k5aWFsxm85AyiI5CJpMRGhqK1WqltbUVk8l0x88PEYRWq0WhUDB9+nSXq49UXl7Ok08+SVBQEM899xxRUVEu6TUNDQ3llVdeYcmSJfz4xz+mpaUFi8XitPYEBASQl5fHH//4R7q7u+/42UE2RFNTE/v27WPx4sXExcW5lO2wZ88etm/fztatWykvL+fChQuo1Wq8vLxcckosEokIDw8nIiKCN954A6FQSHBw8KgMu8lGLBajUCh49913efDBB+9Yi2KQICorKykpKWHDhg0ulWBTWFjIsWPH2LRpE8nJyZw7d462tjauX79OTU0NOp0OmUyGQqFwGRHbHESBgYFERESwc+dOuxHqaFEIBAL7kBEYGIhSqbztarXdYjSZTDQ1NREeHu4yCblWq5VDhw5x5MgRHnnkERYsWGCvS9nV1YXFYqGpqYmbN29SWVlJcnIyixYtwtvb2yXaLxAI8PT0ZOHChZhMJg4dOoRIJHJKQLK7uzuZmZl88cUXBAYG4unpOezn7I9TZ2cnarWaFStWuMTN7O/vp6qqip07d5Kfn8+iRYtwd3dHKBTaC5JKJBIkEgkajYYLFy5w4sQJ2tranGbA3Q6JRMLy5ctZsmQJR48e5dKlS05pw5w5c2hubqalpeW2n7MLorq6Go1G4xLeNluBkZdeeol169axZMkSezcrFouJi4tDLBbT09ODVCpFJpPh5eXF5s2bRzXXdgYCgYDc3FyWLl3Ke++9h0ajcfj1pVIpsbGxdHR0YDabh/2c/c599dVXeHt7ExIS4rBG3o7Ozk6KiopYunQpixYtGlQ0QywWM2PGDGQyGWazme7ubhQKBfn5+URHR7uMl3A4hEIhDzzwACtXruTZZ58dd1TTRFi1ahX19fU0NDQM+75dEEajkYiICJd4ui5evMinn37K+vXr8fDwGDSEiUQiIiMjcXd3JyYmhoKCAmbPns3Bgwfp7u52ueHiVmQyGenp6SxYsIA333xzwkGxY2XatGkYDAa6urqGfV9otVqpqalBIBAwbdo0hzZuOK5cucKJEyfYunUrwcHBQzxrAoEAmUxGdnY2P/rRj1ixYgXp6enIZDIKCwvp7Ox0aVEIBAL8/f155JFHOHr0qMOHDm9vb0QiEbW1tcO+L4TvppshISFOX8SyWq2UlpYil8vJyMi4rXErEAjIzMwkJiYGX19fIiIiWL16NZcvX6aoqMjhT91YkUgk9rCCI0eO0NHR4bBru7m54efnR1tb27DvC61WK42NjcyaNcvpgrAV9Zw/f/5tp0U2xGKxfXiTy+UsWrSImTNncv78eb799luMRqMjmjxuFAoF69evp6ioiIsXLzrUk5mcnIxEIkGn0w15Twhw5swZxGKx013V27dvJzAwkLS0tDEfKxaL2bp1K35+fhQXF9s3PXFVbHt6PProo6hUKgwGg8OuHRAQgF6vp6ysbMh7QgB/f3+XKK3b3NxMcnLyuD15YrGYvLw8LBYLBw8eHHEhxxVYtmwZZWVlfPXVVw67ZmBgINHR0cMOVcL6+np8fHwcXg/x+/T39/Phhx8SFRVFTEzMuGc6AoGAmJgY5s2bR3NzM7t27brtfNtV8Pb2Jjw83KHOKrlcjlKppLGxcch7wosXL6JUKp06XBiNRg4fPsy8efMmbMfIZDLmzZtHQkICp06doqKigr6+vklq6eQjFotJS0tDq9VSU1PjkGvaan8NK4irV68SEhLidPvBYDAQFhY2KSmCQUFBZGZmEh4ezq5du7h586ZL9xSxsbH4+fk5dNhwc3Mb9kERdnR0kJSU5LQhw2w2o9VqeeihhybVjpk2bRqbN2+mq6uLM2fOOHy+Pxa8vLyIi4tz6LDh4+ODh4fHEG+psLW1lWnTpjktebetrY2//OUvxMTETOqysM0BtHbtWs6cOUNZWZlTg1TuhC2t35EzDds2lc3NzYNEIbStDjprhbOvr4+KigoiIyMnfdhyc3Nj6dKlREVFcfjwYU6ePOmyXsyoqChmzpzJtWvXHLLGIZFIkEqlXLx4cdBwKnRmvB98F7Kn1+vx9fWd9HUUoVCIQqEgNzcXd3d3jh07Rl1d3aReY7Lw9PTE29uboqIih9g7IpEIuVxu3/nQhlAikTg1/sFkMtmzn6aqHfHx8eTn5yMUCjl27Bi9vb0u11NIJBLkcjkXLlxwmCBkMtmQeyF0d3d3qiAkEgmzZ8+e8kzr1NRU5s2bR11dnb3KvCthC7drbW11iK0jEolQKBT09/cPFoQz6z1YrVbkcjmZmZmjFoRtC0STyTSmsVYsFjN37lzi4uL46KOPaG9vp7+/H6PR6JS4hFuRSCQEBgai0Wgc0nuJxWI8PT2HCsLLy8tpMRA9PT00NDTg4+MzKlH29fVx4cIFtm/fzq9+9asxl+ILCAggIyMDq9XKa6+9xurVq9mwYQN79+4d71eYdIxGo8MEoVQqh/SUYlstBGdgMBjo7u5m+vTpoxKEVquluLiY4uJi5s6dy/Tp08d0PZFIREBAAIsWLeLo0aO0tbVx4cIFrl+/jlQq5cEHHxzvV5k0HDU1lkgk+Pj4DOkdxc7MP+zv76enp2fUguzp6eH48ePMnDmTrVu3jqkQho2+vj6OHj1KXV0dfn5+dHd309jYyJEjR0YtCKPRSFtbG+fPn6e3t9f+d09PTx566KEJpT86ytgVCoV4eHgMuZ5Yr9c7pAHDMTAwMKa4BbVazfXr1/nTn/5EYGDguHo2g8FAQ0MD1dXVxMfHo1Ao8Pb2Ziz3wWKxcOXKFf7xj3+gVqtpbW2lr6+P+fPnk5OTM+Y2OQOLxYJOpxvSM4u7u7ud5sGTSCQoFIpRPxW2KVJAQMC4ZyVKpZL8/Hxqamqorq4mKSmJpKQkYmJiRn0OqVRKVlYWWVlZ6HQ6/u3f/g1PT09effXVcbXp+zjKwDeZTKhUqiH3UdzT0+M0QUilUnx9fUd9fZ1Oh1KpRCaTDblxo/W2+vv78/zzz3Ps2DEGBgbw9/cnKSmJF154YVzfobGxEavVyty5c8d1/K04qtCZ2WxGrVYPGd6Eer3eaU4auVxOYGCgva7TndBqtfT09LB8+fJBN81qtVJbW0tubi6tra0jnsdW22HOnDkEBweTm5vL1q1bx+02r66uBiAxMXFcx9uwWCwYDAaHpVDaFhVv9UOJb52HOhKpVIpCoaCiooLY2Ng7ftbNzY2VK1eSlpY2SNW1tbW8++676PV6RvK6Wq1WOjs72b17N2q1mtzcXB544IFxGac2KioqMJlME95b02g0cvPmTZRKpUMEMTAwgF6vRyqVDrqeU9cyRCIRAwMDnDx5ckTPobu7OwEBAUMys9zd3Zk/fz7Z2dl3LBdotVrp6Ohg//79nD17luXLl5OTkzMhMQwMDHD9+nX8/PwmHD5g29k3IiLCIcPGwMAAfX19Q/JexG5ubk51Xdss9vHaMbbUw4iIiNt2+7ae4cCBA5w7d460tDTWrl07KT+iXq8nICBgQueB72Y/Wq12SA84VZjNZvR6PQkJCYMeMGFYWBjguPnvrUilUjQazbirrNiykGJjY297I3t7e/n00085c+YM8+fP59lnn52UgCCDwUBfX9+w+bADAwNjcol3dnbS0dHBQw895JDoNZPJhNFoZM6cOYPSH4WBgYHU1NQ4Le7Qw8ODsLAwGhsbxxUlrVaraWhoGGIcwXciN5vN/OMf/+Dbb78lOzubdevWTUqPaLVaqaurIzY2dlj74euvv6akpGTU57tx48Zt8y2nApsAb/XnCIODg50qCG9vb9asWUNXV9e4ViB9fX3JzMwcYhxZrVZUKhX/8z//w7Vr11i5ciX333//pO0AJBAISEhI4De/+Q1xcXGDrrtt2zb++te/DpsIMxwGg4HOzk5CQ0MnpW2joaenB4PBMMS5J4yPj6e9vd1pmU6enp5kZWXx5Zdfjqt6u1Qqtecr2rBYLLS1tfHZZ59RU1PD8uXLWbp0Kb6+vpPZdDw9PQkKChpU/MNWw3L27NmjLoam1+tpaWlh/vz5k9q+O2EymYYtxSScNWsWarXaaYKQSCR4eHhQUVGBWq2e8FK0rQrvwYMH+fbbb8nKymL58uUOS1MUCoU89thjzJo1a9S1Ni5duoTBYBhXxtp4sA3Nw3lnhSEhIXR2dqLVah3SmOEQCoXExsZSXV09oUBTq9VKV1cXu3fv5tKlSyxbtoy8vDyHl+/R6XT2gJeRsFWbFQqFkzJbGQ1arZaWlpZhhyghfKeY0Y53U4FUKuXpp5/m5s2bEwqXNxgMvPvuu1RVVZGdnc2aNWucsrTf1NSEl5fXqGYytlpZixYtckDLvqOjo4ObN28O24MJARYuXOjUXkIkEpGYmEhVVRWVlZVjnn5aLBY0Gg3/9V//hVarpaCggGXLljktziMhIWHUruz33nuPpKSkSVsLGQ1Xr161V+K5FaFAILB3186qq2Dbg3LJkiVcvHhxxOKa38dsNtPc3Mzf/vY3dDodWVlZ9q2QnYVSqRzx+gMDA7S3t1NVVUV8fLxD62LX1NTYg3pvRSgQCJgxYwadnZ10dnY6rFHDsXTpUlQqFSdPnhyV59JkMtHc3MyePXtob28nOzubuXPnumQh01vR6XTs2LHD4fWw9Xo9Op2O6OjoYd8XAoSHhyMQCKitrXVqeHpYWBjz5s3j7NmzI4rTJoZ9+/bR1tZGfn4+CxYsGLHQiCtgqwm6e/duVq5c6dBCb7Y8jNvNgOyDbHh4+LidQ5PJ8uXLmTlzJp9//vltp6AWi4Xr16/z8ccf09rayqpVq1i2bNldsZeozWF26tQpnnrqKYfX5WhsbCQkJOS2IrQLYu7cuXR2dk7K/tETwdPTkxkzZlBcXDysO9u2wvjOO+9gMBhYs2YNCxcudFJrx45Op+PgwYPU1taydu1ah/don3zyCf7+/rfdptsuiKSkJAIDA7lw4YLDGjccAoGAuLg4tmzZwq9//WtUKpV9GOvv76empoa///3v9tqUM2fOdOnalN/HYrFw4sQJzp07x09/+tNhI7+mioGBAZqbm+nr62PatGm3XWK3C0KpVBIUFER5ebnTE1c8PT1ZtGgRCxYs4MCBA3R2dqLX66msrGTnzp1IJBKys7OdWsZgrFgsFo4fP05JSQlbtmwhNjbWoWEHJpOJixcvkpaWdsc1k0ET9ejoaHtBcWenznt5efHzn/+c9vZ2iouL+frrrzl06BAmk8neMzhzajkWzGYzly9fprCwkIKCAhYsWODwNvT39/Pll1+yYsWKO67pDAogCAkJITU1lVOnTjm9qq2tNvOyZcvYvn07Wq2W4OBg1q9fz6xZs1yi4u5oMBgM1NfX8/rrr7NlyxZSUlIc3gaz2YxKpaK2thaZTHbHeItBdzUwMJCEhAR27tzp9NmGDXd3d3tmeHJy8l0lBls02JYtW/jVr35Fenq6U2ZCGo2GoqIilixZMqIDbMidDQoKIj4+npKSkjElr0w2BoOBsrIyPvroI4KDg1m9ejVlZWW89dZbQxJUXRGdTkdhYSG/+93v2LlzJ4mJiU7b0K69vZ0jR47w9NNPj+i0GyIIPz8/Nm7cSGFh4bjiEyYDnU5HeXk5O3bsIDw8nPz8fJYsWcLjjz9OZ2cnr7/+Oi0tLU43fm9He3s7H374IadOneKXv/wlUVFROCt2Va1W2xOSfHx8RgzgHSJZmUxGXFwcZrOZ1tZWvL29HWrJazQaKioqOHr0KF5eXuTl5TFt2jSkUqm9ysquXbt47733WLVqFXFxcS7hnbRarfT29lJRUcG5c+fo6+vjiSeeYNasWU5tV1NTE8eOHWPLli2jiuYespGrDaFQSHFxMfHx8Q7zpul0OsrKyigpKUEkErF582b7VgjwXTCNr68vS5cu5eLFixw7dgw3Nzfc3NyQy+UIhUKnPIX9/f10dHRw8uRJvvjiC8LCwigoKCAhIcHhbfk+fX19FBcXYzKZWL9+/ajuzW03gwf48Y9/TEFBAZmZmVM6/lmtVkwmEydPnuTIkSP4+Piwfv36EZNfvvrqK7Zt24ZEIuHZZ58lMjISuVyOWCx2WPZTb28vtbW1HDx4kMrKSv73f//XKTvvDUdNTQ2ffPIJmZmZLF68eFTH3FEQhw4d4vz582zYsGHEzKqJYDQaKSkpYe/evURGRvLYY48RFhY24mzCZDJhNpuprq7ml7/8JXFxcTzzzDMkJiZO+XKy2Wymrq6OP/zhDxgMBp5//nnmz5/vUO/jSO3793//d4KCgvjJT34yam/uHQWhUql488038ff355lnnpkSF7FWq+X06dMcPnyYhIQEHnjgAcLCwsZ0LYPBQEtLCzqdjs8//5yWlhZmz55t38heJpNNylRVo9Fw7do1Dh8+TEVFBfHx8SxdupSYmBi8vb1dwpaB76a75eXlfPHFFzz66KMkJyeP+tg7CgKwn/ixxx4bNsJmIqhUKkpLSykuLmb69Onk5OQQHBw8oUSVmpoaamtruXnzJjqdDq1Wi7e3NxERESQkJODr64tYLMbd3R03N7dBw4tt6LIlsRiNRnp7ezl//jydnZ10d3fj5uZGZGQkXl5exMbGEhoa6lIeU4vFgl6v51//9V9ZvXo1aWlpY4opHVEQarWaoqIiysrK+M1vfmM33iaKSqXi7NmznD17FqVSyeOPP46fn98gW8VqtVJWVoZSqSQ4OHhMT6Ber6epqYnq6moqKyvp7+9HKpXi7u6OWCzGz8+PkJCQQd/HYrHQ1dWFSqVCpVJhNpuRSqU0NTURHBxMfHw8sbGxE870nkp0Oh1Hjhzh7Nmz/OIXvyA8PHxMx48oCPhuH6y3336bVatWDdoycbzodDpKSko4d+4cAQEBbNy4keFqXQ0MDJCXl8eiRYsoKChg5syZE7rujRs3+Oabb2hsbKSrq8tegc5mi8jlckQikT1iesaMGcybN29IEpCrYjKZuHbtGi+//DKvvfYaISEhY04cHtXUISEhgZ///Oc888wzvPPOO3dcPh0Ji8XCsWPHKCoqIjExkfXr1992Wmu1Wmlvb6e9vf2Omd2jJSwsDFsu6w+RmzdvsmvXLhYsWDAkeWm0jLrv9/PzY/PmzXz00Ue33cBrJPR6Pbt27eL48ePMmjWLtWvX3nZ8s1gs9Pf34+bmxrp161xix0BXRq/Xc/78eVpaWvjRj340bmfiqAUhl8vJzc1FKpVy4sSJO+4kZ7VaMRgMfPLJJ9y4cQOz2UxXVxcHDhzg9OnTpKWlkZubO+wwYaO/v5+vv/6ajIwMwsPD75ogGBtWq5Wenh6uXr065NXe3j6p1zKbzRw/fpxTp07xk+ufwtAAAAiwSURBVJ/8BE9Pz3HbeaP2NonFYnx9fcnJyeHvf/87fn5+ZGRkDDsjMBqN1NTUUFJSQmtrK4sXL6a5uZny8nJSUlLIzs4esUvr7e3l0KFDzJgxwyX2AxsrVquVyspK/va3v2G1WlGr1fal5+nTp/O73/1u0q5VVVXFuXPnyM3NJSkpaULnGpP7USgUkpyczOrVqykuLiYiIoK4uLghP2xvby+nTp2yb9Le0NCATCYjKirKXqhjJAUbjUbKy8tZtWoVMpkMk8mERqOho6MDoVBIeHi4y0dLKZVKMjIyMJlM/PWvf2X+/PksWbJk0sLuBwYG6Orq4tNPP2XmzJnMnj17wucclz965cqVdHV18eabb/Lb3/6W4ODgQT+wTqejvr6egYEB3N3dMZvNuLu78+CDD4562ioWi1m2bBnTpk1DLBajUqnYtWsXly9fRq1W89vf/pakpCSXjY0QCoXMmDGDpKQkNBoNr7/+Oo888gi5ubmTcv6BgQE0Gg3btm0jMDBw0rLbx303c3JySEtL49e//jUajcYecjcwMGAv5unh4UFoaCgmk4mrV6/ywQcfoNfrRxWe5+/vz4svvmif0dTW1tLf389//ud/kpGR4dQSBmPBViDUzc1tUt3parWanTt30tzcTH5+/qTNnsYtCA8PDzIzM0lLS+P3v/89bW1tWCwWuru7KS0txWw2Y7FYuHbtGlqt1p66Vl5ePqpKMQKBYFAMQXJyMhs2bECr1fLll1/i4+NzVxiaFosFlUqFVCoddb2Ikejo6ODAgQNUVVXxwgsvjLuq73CMewlTJBLh7+/PmjVreOedd9izZw95eXlotVp77Uar1YqnpydhYWFER0cTHh4+rM0xWpqamti7dy9PPPEEUVFRLjtcfB+DwcCVK1dISUmZlLWO7u5uiouLqaio4IknniAsLGxSq9ZNaE1bIpEQEBDAk08+yfvvv09JSYl9y+iUlBTCwsKIiYkhLCwMf3//cfv8LRYLNTU1vPvuu6SnpzNnzhzkcvld4T3s7e3l9OnTLF68eMKzpc7OTruH9+GHHyY1NXWSWvn/mHCQg0QiITIykvXr1/Pxxx+j0WjIyMggPT0dpVI5KU+xLadBq9Wi0+koLi6moKDgrhgy9Ho9Z8+e5amnnrLbEGazGYPBYN9AZqQn3GZAHjhwgAsXLlBQUMDSpUunpL2jWssYLdevX+fDDz/k5s2bvPzyy6OK4fshY7FY+Oabb3j44Yc5e/YsoaGh9io3RUVFCAQCVqxYcccNZGw+jG3btlFZWclPf/pT7rvvvilr86QKwuaR3LdvH0ePHuWNN94gKCjIadHGroDRaEStVuPn54dIJKKnp4f9+/djtVqZN28eJ06c4KGHHrptNlVLSws7duxApVLx3HPPERgYOKU946T+UrZl5by8PHx8fHj11VfZunUrcXFxDi2I4UrcWmtKJpOxePFixGIxarWazs7OYWddJpOJb775hv379xMeHs66deumXAwwyT2EDYvFQm9vL0ePHqW0tJR58+aRlpb2g15pHAt6vZ6Ghgb279/P/PnzBxU5sVqtaDQaTpw4QWlpKYmJiaSnp4+6ot1EmRJBfJ+TJ0+yb98+YmJiWLFiBZGRkVO6R6er09vby40bN/jnP/9JSkoKK1assK/49vf3097ezsmTJzl58iSbNm1i5syZDq2iN+WCgO/8B4WFhVRVVfGLX/yCsLAwFArF/0mDs7Kyku3btzN79mwyMzPtPUNfXx+tra1s27YNjUbDz372s9uW/ZlKHCIIq9Vqn369+uqrrF+/njVr1ty2aMUPFYvFwqFDh9i5cyfw3ZT9pZdeQiaTsW/fPvbv38+aNWt4+OGHneZncYgg4P/tGGPbs6K0tJS1a9eSnp7u8MKizsS217mtMHtTUxM7duxg+vTpbNy4EQ8PD4ftqjMcDhPE92lpaaG+vt6+5pGdnU1iYuJdE7s4EaxWq929v3fvXjw9PUlNTWXGjBkOLX5+O5wiCPjuxjQ2NnL8+HGuXbtGXFwcSUlJREVF4e3tfVesU4wF2yYuDQ0N1NTUUFNTg7e3N3l5eYSFhblMbIfTBGGjt7eXuro6vvjiC9rb20lNTSUjIwOlUml3fd+tvYYtz0Oj0aBWqykuLqa0tJT4+HgyMjKYN2+ey303pwvi+1y9epU9e/ZQUVHB/PnzKSgowNvbG7FYjFgsvmt6DdtuOiaTibq6Og4fPsyJEyfIzMwkPz/fKbOH0eJSgjCbzRiNRnp6ejh58qR9k/acnBzmzZtHdHS0y09VrVYrly9fprS0lBMnTiAUCsnJyWH58uV4eHjYs8VcFZcShA3bBmG26nMXLlygvLwcd3d30tPTiY6Otmd6O7vLtVqtdHd309raytWrVzl48CAymYylS5cSHx+PXC7H19cXLy+vu6KHc0lB3EpbWxutra3U19ej0+m4fv06SqUSqVRKaGgo0dHRKJVK/P39p9zX39vbS1dXl70yS09Pj30TuZCQENzc3EhMTCQyMvKujBa/KwRhw2Kx0NfXR3V1NTdu3ODSpUtotVoUCgU+Pj6kpqba3eJSqRQvLy8kEglisRiRSGR/2WwSsViMxWLBbDZjNpvtY//3bYD+/n56enowmUz2YN9Lly6h0WjQ6XSEhoaSnJxMaGgokZGRKBQKp/daE+GuEsRw9PX10dTUxMWLF2lvb6empobOzk6kUinBwcHIZDKUSiVyudzu9PH29sbX1xdvb28MBgPd3d2o1Wp6enrQ6XTo9Xr0ej1arRatVktraytisZiIiAiio6MJDg5m1qxZhIaGurQ9MB7uekHYsH0N278CgYDe3l7OnTtHY2MjGo2Gvr4++vv7MZlMDAwMYLFYEAgECIVCe+ifVCpFLpfbN4lPTk4edE4bd3MvcCd+MIIYDltKoS0C3Lbp/K2bz9t+XIFAYH/ZssAdsamqK/GDFsQ9xo7rz4Pu4VD+P3uPQN/RC3qjAAAAAElFTkSuQmCC)
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
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)
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
![](data:image/png;base64,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)
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Pole and polar are one of the important parts of the circle, many questions can be based on these parts. It should be remembered that while writing the equation of polar for a pole, the coefficients of square terms in the equation of the circle is one. If the equation of the circle does not have coefficients as one, then make it one before solving the question.
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Pole and polar are one of the important parts of the circle, many questions can be based on these parts. It should be remembered that while writing the equation of polar for a pole, the coefficients of square terms in the equation of the circle is one. If the equation of the circle does not have coefficients as one, then make it one before solving the question.