The eccentricity of the ellipse with its center at the origin is . If one of the directrices is x = 4, then the equation of the ellipse is
3x2 + 4y2 = 12
Find the equations of the tangents to the ellipse 3x2 + 4y2 = 12 which perpendicular to the line y + 2x = 4.
Find the equation of pair of tangents drawn from the point (1, 2) and (2, 1) to the ellipse .
A tangent to the circle x2 + y2 = 5 at the point (–2, 1) intersect the ellipse at the point A, B. If tangents to the ellipse at the point A and B intersect at point C. Find the coordinate of points C.
If the line 3y = 3x + 1 is a normal to the ellipse , then find out the length of the minor axis of the ellipse.
If SK be the perpendicular from the focus S on the tangent at any point P on the ellipse , then locus of K is
The tangent and normal to the ellipse x2 + 4y2 = 4 at a point P(θ) in second quadrant, meet the major axis in Q and R respectively. If QR = 2, then cos θ is equal to
If latus rectum of the ellipse is equal to
Find the locus of the point of intersection of the tangents to the ellipse , if the difference of the eccentric angle of their points of contact is 2α.
In an ellipse, the distance between its foci is 6 and minor axis 8. The eccentricity of the ellipse is