If one of the diameters of the circle, given by the equation, x2+y2−4x+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 a2x2+b2y2=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 2a2˙
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 a2x2+b2y2=1
Find the condition on aandb
for which two distinct chords of the hyperbola 2a2x2−2b2y2=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 2x2+2y2−x=0