Question
The curves
and
intersect orthogonally, then
Hint:
We are given two curves. They intersect orthogonally. We have to find the relation between the variables.
The correct answer is: ![fraction numerator 1 over denominator a end fraction minus fraction numerator 1 over denominator A end fraction equals fraction numerator 1 over denominator b end fraction minus fraction numerator 1 over denominator B end fraction](data:image/png;base64,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)
The curves are as follows:
ax2 + by2 = 1 ...(1)
Ax2 + By2 = 1 ...(2)
We will take the derivative of equation (1) w.r.t x.
2ax + 2by
=0
2by
= -2ax
![fraction numerator d y over denominator d x end fraction equals fraction numerator negative 2 a x over denominator 2 b y end fraction](data:image/png;base64,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)
This is this slope of first curve. We will call it slope1.
In the same way we will take the derivative of equation (2) w.r.t x
2Ax + 2By
= 1
![fraction numerator d y over denominator d x end fraction equals fraction numerator negative 2 A x over denominator 2 B y end fraction](data:image/png;base64,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)
We will call it slope2.
The two curves are orthogonal. So, the product of their slope is -1.
Slope1 × Slope2 = -1
![fraction numerator negative 2 a x over denominator 2 b y end fraction cross times fraction numerator negative 2 A x over denominator 2 B y end fraction space equals space minus 1
fraction numerator a A x squared over denominator b B y squared end fraction equals negative 1
space a A x squared space equals space minus b B y squared
space space a x squared space equals fraction numerator negative b B y squared over denominator A end fraction space space space space space space... left parenthesis 3 right parenthesis
space space A x squared space equals space fraction numerator negative b B y squared over denominator a end fraction space space space space... left parenthesis 4 right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK0AAADXCAYAAABoFtHkAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAACALZwRvgAADr9JREFUeNrtnWFkXdkWx7caEU8MFVEVFaJGVUV4H6rqqUeNiIooo6LiiVCjakSVfqgYT5Xoh6jql6qoJypExVMVQ1RVjSojIup5Sj39UBWlH6pGVcg7f3edZmeffc49595z7917n/+PTe8+Ozcz66zss/beZ/2XUuVxMmoPo/Ypal+jthG186q6NGuPGUVazrOoTUStRz4fjdrv0kd7FLPHOXH07+hW7Wcgaps0QyF77Jcxa1Ebp8k6wxdL376o/TNqW9qjc8AYMx21OcvPXpdrIdlD567Mxv+I2h3L9VDt4gwn5JFo8jhqt2VWgQMvp8wq61E7oH2eSrmRvttDv/5Y/o3/7zcp40KzizN0R+2lLEh0JsRJdf4VtVHLd4xEbV7+fTpqTwK0Rwzi1z+idshwziOB26VUdnK0rLjs31H70XLtqcwo5qJlIOW7ENudkhCiN0B7xPwatStG342oXXTcLkEwKDfocMr1PyUk0OPbzxnfNyNx71Cg9lAym65b+uGUjwK1izPA+Pei9peMMR+MzydTblh87aE8CicCtQd4njF727a+fLeLMxyQWLXe3uI7ie9iZuUG2GaoR3LDeyTe6w3QHheidivj+pIR7/tuF6d4nLJosG3N3JWwAHHsg6itGmP6pE+/GWeithiYPQ6q2p5sT8aYac2pQ7CLNws3k2syC83KrIv92njLqytqK1HrT5l1RgKyx7I4XRaww+uA7JKXH8Q/Nlz9D+zj3zwxWJTQaYemID4+wSvFNWlFrxE6rXOOS4fNH3/vdNhxKhse6E5Khw1opt3xuOV13LUCDrsTQAth9q70Qqyo0zI8YHjA8IDQabkQo9NWxmHpuHRaQtoWZzdM0dRo8/3ZUGkkZRz5YttRe6tqqTV4e+sg/bV8iqRG48XnTdrFymGVfBkEb8Ddp4u1h7TUaLy5tUS7WIFtHhh9Zy19pIXYUqN/lcUO0sXfy5inxiNwQdXEKUyQTnIjULvEtrlq9CHBc6QCNnGCtNToZYnVcHPidPF5Y/ZFfv9N4+fwVj7eIe0N1C6xbcbFJsPiqDMVsIkTZKVGv5bYTud7WazEjKpkSjlmodmA7RLbJl4Vf1Z7X+IO1SZOkJUavU92Dmw3U3dazByvtM99Mjt3B2qX2DZxBjIyEqBd8ELV3tYP1SZOUC81+rjEr7ZHpikuoTv3vPJbMTBPyvhxiw3OGyFBSDZxgjyp0djqsW3fXLY85p7LzR6UGWVfwHaJbbNg9E3Kz4ZmEyfImxoNra4pow+Pwk2V3EDHqnlM1bZ7JgO3S5ptFtTePd0QbOIMeVPFV2SxcVo+90vfVMpWzoLy+yAir11i24xo8epPqnbQ0BWYTZwh7zuXWzJTwHG35aak6a2Oy8+PVcAu4KN2Dfu4SyqZGh6CTYJmTFbPhDbxhlWVVFKkTWgTZzmmdoWECW1CCCGEEEIIIYQQQgghhBRGr+qCVJXDNAnxBbw/isJv6zQF8Y0vNAHxCVQsfEYzkFZTVi7TQYlpB2lS0krOKXtZzKIgK/Wxoq4VaTFIm0ZqCNS2x5ucYfEu6fc0KWlk9Q45oy21qwI4kDEepUORmAd1lDuW6yiXOWfpvy7XYuCwR2h+0gh4PN9Wu3JGyxkz6Am1+9IyslLfpIxbl+sxUxYHd63gBfGECZWU5UFK86hlLOJXVMI+ZDinbbZEBuq8/BtZuk9oalIWT1UyP+lZSngAjakrRh+U/S6mfDdi3lMSblBMjZSGqd6ta0/pHFH2Eys45aOU756RGHmIZiZl8sH4fDLFOZ+r9Fx/29ZXLPE+r9IVsglpiHdqr0LfrDibDsqa38r4jiUjBh6U2Rc6Vz0SBzM8IKWBbai7EhYgjoWe1Kp2HXupm2q3voCNac2p++TndSc9E7VFmpqUyTXZQZiVWRf7tfGW17I4XRaQ+YEkEvSpVlRS9ieejUcCs9sPYrMNulDn6aMJcrEooRP3l4l30GkJnZaE6yiulICn0xLOtKSxWcqV5sNsTaclDA8IodMSQqcldFriVUzqs7oMMy8qCtVliLdQXYZ4BdVlSFOY6Tf1ZkdUaHyralm5ePG7qOgG1WVIU2AxtFlgrPkeKV4ov1/g91FdhjQNXvxeKjD2gdF31tKXNcNSXYY0DVLEkcUAtZn38vh/mjITYuxVow96CchOQEXtc5afQXbuDfk31WVIKSxLbApnjNVm5lNm31iFBmOGxVFjFUXIJd00xiPJESk5ce4Y9zhJKcCpjhp9eHx/ShkbO9tntTf/a1QlVWswM8/SxKRM9snOgUm3xWl1QQ8kM0L26IUsrJTMpq+08X0yg3fTzKRMjkv8agLJpCeWsWbfeSMk0P8A5lV5AsyEfAMqMLbtqsuWx/qExLA6k1G7p32GIs2gtDcq/94vIbmB1OeU0YdH/6Zl98A2dkHtlT/CTsKYqm2BTdK8pBWsyOLqtHzul76plLEjWrz6k6odNHRpY2bEkTdpWtIqtmRmhONuixOmCSt/1HYOsJe7pJKqMuNyfYymJb4wJjsKhHjDqkqKNRPiLMfUbl0GQgghhBBCCCGEEEIIIYSQ0ghBGol2qyiURqLdvIXSSLSbV1AaiXZrC2XlfYUijURJKcc5p+zVx4sSijQSJaUcZ7/coDWVnt2Qd6YIRRqJklIdWIVCCmlLZk/MAgMZ41G1HEmMUJK5Y7mOquRzlv7rci0mJGkkSkq1GTxmbqtdKaTljBn0hNp9wfuAxGM21uV6zJTFwZuRRnKpJJNSlJRqKxMqKWGEv/pRy1jEr39E7ZDhnLa/+hG5aQAZvk8CtyMlpdrIU5XM5XqWEh7AeFeMPjyyLqZ895psyWxos4TLNDp7U1Kqw9s0ulF1jij7ycsp2a5RKXEYYuQhhxysFVBSqs18MD6fTHHO5xnOYdv6wvc8FKNPVCDEoqRUG3lnPHpmxdl0LkTtVsZ3LBkx8KDMvlhA9Egc3BuwDSkp1WawDXVX/poHxFCr2vWDYvyejO+Y1py6T35ed9IzUVsM2IaUlOoA12TFOiuz7pba3fJaFqfLol9uWpfclP6U2XgkUPtRUsoB+miCjkJJKeIdlJQiXkFJKUIIIYQQQgghhBBCCCGE5IJSR8RbKHVEvIVSR8QrKHVEmoJSR8QrKHVEvINSR8Q7KHVEvINSR8Q7KHVEOkpRRRpKHdFZvDuepNQR8e54klJH5Bu+HE9S6qh5MEnNFRg/p9IVODuGT8eTlDpqjiHVmODI76o1KpsN4dvxJKWOmgP3elj7/HdV24v+U2wEu95SSWHCv0oo1XF4PFktqaNhcVodLGrPGk8fjPvN8vPPxXk7OsPyeLJaUkfYNbmUc6xtz/uXgrHwt5V+vWo3Vaxg0yhVkzrC7Pm3HOMQKv7X0m/bVqxL3mo3VatgQ/LPnl0Z1w+IryCutRWk6UqZgVMpUu2mahVsSD62c05CWQcsX4v8wiLVboCrFWx2Amy+O23MfnlyvxTfadpp81a7ialKBRtSXngQ0yOO23R4kLfaTXytKhVsSH7WxDfy8KWMhVieajfxyq9KFWxIfvJueQ3JYszkkkq+f5xJvWo3oIoVbKqILQTL02c7XMC6CMfb34lv4YTsf6r2grxJQ4cLWdVuqlrBhk5brO+Fsc7Bvu1jCQfitCVb1aTSjnFZ7aY+fD82+ej3/oWZkEHSoq3UatX5WRU7jkUce4Fmaz3Yc9yUFfM4zUF8AIvWCVlQ3KE5iOucULsvwuA8/Q1NQlwG8Sv2pg9pfTiEoeAGcRboFlwx+qAWc5GmIS5yRNmPtvHyxyOah7gINr/TXuDh1hdxDuwj3sq4jlPBUZqJuALy3bAn25MxZrqOUxPSVvA+xpk6Y/BOxmuaihBCCCGEEEIIIYQQQgghhBBCCCGO4GtJK0K8K2lFyDe+0ATEJ3wqaUUcxNTxrTc7Qmj4raqlmSOPrGilH99KWhHHwGJos8DYDaMPypT3C/w+lrQiTQP5o6UCYx8YfWctfVkzLEtakaaB5gHkUFG26r3ala48mDL2qtGHwiuQREXZ0XOWn4EC4w35N0takVJYltgUzhiXrZpPmX3jclYYMyyOGsuCQv/LVLyGsjpyzGLBataZIKUApzpq9OHx/SllbOxsn9Ve0elRlSx/hZl5liYmWRStoLNPdg5Mui1Oq1cGgoI6aq29kIWVktn0lTa+T2bwbt4Wt5zD9+PI4xK/mtgqshy39J03QgL9D2BeUVHcSXw/joQWrW276rLlsT4hMazOZNTuaZ8hsTQo7Y3Kv/dLOoCvx5GoGTxl9OHRv2nZPbCNXVB7a65hJ2FM1bbAJgO5t5iUisjWzykP1CZ9Po5ckcXVafncL31TKWNHtHgVJYk21N5qhjPiyJuBOKxTBULKirV8P47ckpkRjrstTphWa+GjFsvjybKkkqWsxuX6WCBOi3s7nHH9jLJv25VWiimmrOotPI5MMtbgzOQitqJ3OhDu+49K32tuqOidjbKqt/A40s6qSlZ995V65UVRVGU6w2l/KRgLZ/6irOot0ym/6Lpc028OjyP3ckztFhoJgd9UrTKjDRR4jrf/0py2cCHntC/JU71lXa7HTFkcvJnjyKIHAKQzfDIWmebuykAdp+1S9lPF3BSp3oIV8rz8+3QZfy3ES7ZT+ueMsCFrkvnazH9A0eotiHlPyWq612HD7gTYXHbaIcvirCVO20j1lhn5hUMdcjTiZnjwUiWP7FsSHhSt3oIg+6GECBO8d5VlTXyhyIRTykKsaPWWQZl98R5oj8TBvbx/laTelle9mfaSSr5fXJei1VtwNLlqOClOPBZ5/7zGNgvm6at3uFDPaRs6XChSvQXxx4pKHkvGs/EI733lnBa8yLGuacsxLiF5ceqFGULy8rMqdhx7U9ZSpEPgJW5k6eJtMOy0YN96gGYhLoNjb7z8HWfpxtm4hDjJhEpm1yIzgQWeibMg4dF8zfAZwwPiMqYonZ5CToiTfDA+40iTIsjEad6pvUIbSCl/SLMQl0G2xl0JCxDHIi18lWYhrnNNdhBmZdbFfi23vIhX9NEEjfN//wwFspV5U68AAAYddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93Pjxtbz4tPC9tbz48bW4+MjwvbW4+PG1pPmE8L21pPjxtaT54PC9taT48L21yb3c+PG1yb3c+PG1uPjI8L21uPjxtaT5iPC9taT48bWk+eTwvbWk+PC9tcm93PjwvbWZyYWM+PG1vPiYjeEQ3OzwvbW8+PG1mcmFjPjxtcm93Pjxtbz4tPC9tbz48bW4+MjwvbW4+PG1pPkE8L21pPjxtaT54PC9taT48L21yb3c+PG1yb3c+PG1uPjI8L21uPjxtaT5CPC9taT48bWk+eTwvbWk+PC9tcm93PjwvbWZyYWM+PG1vPiYjeEEwOzwvbW8+PG1vPj08L21vPjxtbz4mI3hBMDs8L21vPjxtbz4tPC9tbz48bW4+MTwvbW4+PG1zcGFjZSBsaW5lYnJlYWs9Im5ld2xpbmUiLz48bWZyYWM+PG1yb3c+PG1pPmE8L21pPjxtaT5BPC9taT48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PG1yb3c+PG1pPmI8L21pPjxtaT5CPC9taT48bXN1cD48bWk+eTwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PG1vPi08L21vPjxtbj4xPC9tbj48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjxtbz4mI3hBMDs8L21vPjxtaT5hPC9taT48bWk+QTwvbWk+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeEEwOzwvbW8+PG1vPj08L21vPjxtbz4mI3hBMDs8L21vPjxtbz4tPC9tbz48bWk+YjwvbWk+PG1pPkI8L21pPjxtc3VwPjxtaT55PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtc3BhY2UgbGluZWJyZWFrPSJuZXdsaW5lIi8+PG1vPiYjeEEwOzwvbW8+PG1vPiYjeEEwOzwvbW8+PG1pPmE8L21pPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1vPi08L21vPjxtaT5iPC9taT48bWk+QjwvbWk+PG1zdXA+PG1pPnk8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tcm93PjxtaT5BPC9taT48L21mcmFjPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4uPC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbz4oPC9tbz48bW4+MzwvbW4+PG1vPik8L21vPjxtc3BhY2UgbGluZWJyZWFrPSJuZXdsaW5lIi8+PG1vPiYjeEEwOzwvbW8+PG1vPiYjeEEwOzwvbW8+PG1pPkE8L21pPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bW8+JiN4QTA7PC9tbz48bWZyYWM+PG1yb3c+PG1vPi08L21vPjxtaT5iPC9taT48bWk+QjwvbWk+PG1zdXA+PG1pPnk8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tcm93PjxtaT5hPC9taT48L21mcmFjPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4uPC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbz4oPC9tbz48bW4+NDwvbW4+PG1vPik8L21vPjxtc3BhY2UgbGluZWJyZWFrPSJuZXdsaW5lIi8+PG1zcGFjZSBsaW5lYnJlYWs9Im5ld2xpbmUiLz48L21hdGg+wSaELgAAAABJRU5ErkJggg==)
We will substitute (3) in (1)
![fraction numerator negative b B over denominator A end fraction y squared plus b y squared equals 1
left parenthesis space fraction numerator negative b B over denominator A end fraction plus b right parenthesis y squared space equals space 1 space space space space space space... left parenthesis 5 right parenthesis](data:image/png;base64,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)
We will substitute (4) in (2)
![fraction numerator negative b B over denominator a end fraction y squared plus B y squared equals 1
left parenthesis fraction numerator negative b B over denominator a end fraction plus B right parenthesis y squared space equals space 1 space space space space space space space space space space... left parenthesis 6 right parenthesis](data:image/png;base64,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)
Divide (5) by (6)
![fraction numerator begin display style fraction numerator negative b B over denominator A end fraction end style plus b over denominator negative begin display style fraction numerator b B over denominator a end fraction end style plus B end fraction space equals space 1
fraction numerator negative b B over denominator A end fraction plus b space equals space fraction numerator negative b B over denominator a end fraction space plus space B
space space D i v i d e space a l l space t h e space s i d e s space b y space B b
space space space space space fraction numerator negative 1 over denominator A end fraction plus 1 over B space equals space fraction numerator negative 1 over denominator a end fraction plus 1 over b
space space space space space space space 1 over a minus 1 over A space equals 1 over b minus 1 over B](data:image/png;base64,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This is the required answer.
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For such questions, we should be careful while taking the derivative.
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What type of ovule found in Capsella
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