Find the standard equation of the ellipse whose foci are (±2,0) and eccentricity 1/2
If the chord joining points P(α)andQ(β) on the ellipse (a2x2)+(b2y2)=1 subtends a right angle at the vertex A(a,0), then prove that tan(2a)tan(2β)=−a2b2˙
Find the locus of the middle points of chord of an ellipse a2x2+b2y2=1 which are drawn through the positive end of the minor axis.
Prove that the area bounded by the circle x2+y2=a2 and the ellipse a2x2+b2y2=1 is equal to the area of another ellipse having semi-axis a−b and b,a>b .
Find the coordinates of the foci, the vertices the eccentricity and the length of the latus rectum of the hyperbola 5y2−9x2=36
From the point A(4,3), tangent are drawn to the ellipse 16x2+9y2=1 to touch the ellipse at B and CE˙F is a tangent to the ellipse parallel to line BC and towards point A˙ Then find the distance of A from EF˙