Maths-
General
Easy
Question
Through the vertex
ofthe parabola
chords OP, OQ are drawn at right angles to each other If the locus of mid points of the chord PQ is a parabola then its vertex is
The correct answer is: ![left parenthesis 4 a comma blank 0 right parenthesis](data:image/png;base64,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)
Related Questions to study
maths-
The area of the trapezium whose vertices lie on the parabola
and its diagonals pass through
and having length
units each is
The area of the trapezium whose vertices lie on the parabola
and its diagonals pass through
and having length
units each is
maths-General
maths-
The Locus of centre of circle which touches given circle externally and the given line is
The Locus of centre of circle which touches given circle externally and the given line is
maths-General
maths-
If the length of tangents from
to the circles
and
are equal then ![10 a minus 2 b equals](data:image/png;base64,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)
If the length of tangents from
to the circles
and
are equal then ![10 a minus 2 b equals](data:image/png;base64,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)
maths-General
maths-
The line
cuts the circle
in
and Q Then the equation of the smaller circle passing through
and ![Q](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAOCAYAAAD0f5bSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALtJREFUeNpjYMAO3IB4BxB/A+IfQHwYiB0Z8IAOIN4AxKZAzATFfkD8EoitsWnIA+KZOAwD2XQcXVAWiK9ATcYFPgAxG7JAKxDnMOAHu4HYAFkAZIs8AU0PgZgLxmGChhQ+wAJ1HorAJwKagoB4IbrgNwKBcBTdPwxQUxJxaKgE4i5sEhpA/BiI46HOBQE9IF4MDVmcwByI90OTDgj/B+IsBhJBOBA/B+IzQJwMxKLEauQB4nIgvgZNyAwAqaghgYyCZAkAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlE8L21pPjwvbWF0aD715aU4AAAAAElFTkSuQmCC)
The line
cuts the circle
in
and Q Then the equation of the smaller circle passing through
and ![Q](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAOCAYAAAD0f5bSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALtJREFUeNpjYMAO3IB4BxB/A+IfQHwYiB0Z8IAOIN4AxKZAzATFfkD8EoitsWnIA+KZOAwD2XQcXVAWiK9ATcYFPgAxG7JAKxDnMOAHu4HYAFkAZIs8AU0PgZgLxmGChhQ+wAJ1HorAJwKagoB4IbrgNwKBcBTdPwxQUxJxaKgE4i5sEhpA/BiI46HOBQE9IF4MDVmcwByI90OTDgj/B+IsBhJBOBA/B+IzQJwMxKLEauQB4nIgvgZNyAwAqaghgYyCZAkAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlE8L21pPjwvbWF0aD715aU4AAAAAElFTkSuQmCC)
maths-General
maths-
If the angle between two equal circles with centres
,
is 12
then the radius of the circle is
If the angle between two equal circles with centres
,
is 12
then the radius of the circle is
maths-General
maths-
The equation of the circle passing through the origin and the points of intersection of the circles
![x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 2 y minus 4 equals 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAATCAYAAADWFkxaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAspJREFUeNrtWt9HnlEcP5IkM5Iku4jXa5LpPl1MJMm8MmYymXQ3u3jvk11MTBevJJFJZmYkmclu5jUzkzGTZBejP6CbXXSRJOr71efV4+k8dc7zPOeHp/Phw/uep+P5nM/5nnO+5/smhD7OwBPiT2JZuIEvOgIKhCbiC+KfoCOgaDgOOgKKhIfE70FHQFHQjVy2dIt0PEIe7xqDxA3iIe4UO8RnHsWGaZ/uEpeJv8AVtGXCfeIWAsolbOq4Q/zrSVDzqTQBTYw+LOwJD7TZ8KlOrMQWUT3rzvgl5crIc6C2dfBuMO1JUMvQQ9z1QIdpn54QFyXtC7JFzULeSP74NZ41wIHUm1KQ6kBXiU8l7VXinEUd0eO+fkNfVf9sXpZVfMw7Lapn2DhUwGnXiKR9CM+ugMtiXZHvU8QlSUDEmXcwPSfOx9raiP+IHRZ1MFqwA/Yo9FXxzxQGkILo+pgXdHxKmj+V+fyPd8nefyDrMEqs4fNw1jwlQzCNEddjba+Is5Z1COy+LxX7mvYvCa24MA1a9jGtT1lwes2zk6QHX8VFiWwnh9WcdjXye/ci3zuJ+5g8mzr6JbvfTZOl419aXVG0Ez8lHMm6Ptr0yURQJ/5WUUXE9xsQpDPQo8jnGnTZ1sG7X1mzr0n/4ighoMuOfMziU9oFdJCQfrQmpR+N+mfNUHlIJ6h/YNJK2F2aHOjQNd20f1HwJfktcmRXPqb1KetFcVTSPiK7KPKgP8MkrjX+NnCZ0BngO3FRi/xAnHSoQ7WvDf8a6EKu3OzYR1MeX4fHWMxxrMU3kk6UyKKTwAXt9w4HWkVJatczw2V9bfnXwJZQL2ea9NFFUDO+YVzNSEVmROzfJLhxk3hP0vljwlZvA+MwpiL8wpmklGTbP52j3pWPJoO6HQv1GHeGFXH566rX4EnYFgHBxwKBj/OBYEPwsSh4gLwxIPiojXOrRRBDXYg1OAAAAO90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1zdXA+PG1pPnk8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj40PC9tbj48bWk+eDwvbWk+PG1vPi08L21vPjxtbj4yPC9tbj48bWk+eTwvbWk+PG1vPi08L21vPjxtbj40PC9tbj48bW8+PTwvbW8+PG1uPjA8L21uPjwvbWF0aD7cLuVjAAAAAElFTkSuQmCC)
The equation of the circle passing through the origin and the points of intersection of the circles
![x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 2 y minus 4 equals 0](data:image/png;base64,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)
maths-General
maths-
The locus of a point such that difference of the squares of the tangents from it to two given circles is constant, is given by
The locus of a point such that difference of the squares of the tangents from it to two given circles is constant, is given by
maths-General
maths-
Radical centre of the circles
![x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 6 y plus 4 equals 0](data:image/png;base64,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)
Radical centre of the circles
![x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 6 y plus 4 equals 0](data:image/png;base64,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)
maths-General
maths-
The radical axis of circles
and
‐5x
is
The radical axis of circles
and
‐5x
is
maths-General
maths-
If the circle
bisects the circumference ofthe circle
then ![k to the power of 2 end exponent minus 1 equals](data:image/png;base64,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)
If the circle
bisects the circumference ofthe circle
then ![k to the power of 2 end exponent minus 1 equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD4AAAARCAYAAACFOx+nAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAPVJREFUeNpjYCAN/IfiX0B8FIhVGEYYYALiLCA+xzBCwY+R6Gl7ID44XDzzDZqMCQFJaB5XoqFb1IC4Fogv0NrToILqEpEO2gL1PC3BYiBOgxamNAUBQLyciJjeBsR8dEyFNPd4PRCXQ9ksQLwQiL3Q1IA8rUHn7Edzj6+CxjoHlO2Ipx5HxoPB4/+JwDjBLSDWAeJNQGw+iApcmgYuE7REPw71PLUcTHYs0MvjoBjeD8SRQDx3kFWxNE3qIA/Ph7J7gDhjpCT1SdA6EwZ2A7H1SPD4OrSqSxCIT9KhkTLgHn8HrcaQAaiQ24tFnJ4epnfVOfwBAHGoUDiMTneHAAAAfnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtaT5rPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4tPC9tbz48bW4+MTwvbW4+PG1vPj08L21vPjwvbWF0aD7iFjIaAAAAAElFTkSuQmCC)
maths-General
Maths-
Two circles of equal radii
cut orthogonally If their centres are
and
, then ![r equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAKCAYAAABBq/VWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFpJREFUeNpjYECAeiAuB+IMID4DxD+gfKqCVUD8FIh7gFgJj7r/RGCc4BYQBzHQEDAB8TcGGgNzIN5PpFqygysSiOfT2ieTgDiZ1pasA2IvWlvyDog5GIYyAACwWx66pgU/iwAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+cjwvbWk+PG1vPj08L21vPjwvbWF0aD7WCX2yAAAAAElFTkSuQmCC)
Two circles of equal radii
cut orthogonally If their centres are
and
, then ![r equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAKCAYAAABBq/VWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFpJREFUeNpjYECAeiAuB+IMID4DxD+gfKqCVUD8FIh7gFgJj7r/RGCc4BYQBzHQEDAB8TcGGgNzIN5PpFqygysSiOfT2ieTgDiZ1pasA2IvWlvyDog5GIYyAACwWx66pgU/iwAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+cjwvbWk+PG1vPj08L21vPjwvbWF0aD7WCX2yAAAAAElFTkSuQmCC)
Maths-General
maths-
The number of points such that the tangents from it to three given circles are equal in length, is
The number of points such that the tangents from it to three given circles are equal in length, is
maths-General
maths-
The angle at which the circles
intersect is
The angle at which the circles
intersect is
maths-General
maths-
The eccentricity of the ellipse which meets the straight line
on the axis of X and the straight line
on the axis
and whose axis lie along the coordinate axes is
The eccentricity of the ellipse which meets the straight line
on the axis of X and the straight line
on the axis
and whose axis lie along the coordinate axes is
maths-General
physics-
A point source of length S is located on a wall. A plane mirror M having length l is moving parallel to the wall with constant velocity v. The bright patch formed on the wall by reflected light will
![](data:image/png;base64,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)
![](data:image/png;base64,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)
A point source of length S is located on a wall. A plane mirror M having length l is moving parallel to the wall with constant velocity v. The bright patch formed on the wall by reflected light will
![](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General