class 11

Math

Co-ordinate Geometry

Conic Sections

If one of the diameters of the circle, given by the equation, $x_{2}+y_{2}−4x+6y−12=0$, is a chord of a circle S, whose centre is at $(−3,2)$, then the radius of S is :

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Find the locus of the point of intersection of tangents to the ellipse if the difference of the eccentric angle of the points is $32π ˙$

If two points are taken on the minor axis of an ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is $2a_{2}˙$

Find the centre and radius of the circle $(x+5)_{2}+(y−3)_{2}=36$

Find the eccentric angles of the extremities of the latus recta of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$

Find the condition on $aandb$ for which two distinct chords of the hyperbola $2a_{2}x_{2} −2b_{2}y_{2} =1$ passing through $(a,b)$ are bisected by the line $x+y=b$ .

Two circles are given such that one is completely lying inside the other without touching. Prove that the locus of the center of variable circle which touches the smaller circle from outside and the bigger circle from inside is an ellipse.

Find the equation of the parabola that satisfies the following conditions: Vertex $(0,0)$, focus $(−2,0)$

Find the centre and radius of the circle $2x_{2}+2y_{2}−x=0$