If `P_1` and `P_2` are the lengths of the perpendiculars from any points on an ellipse to the major and minor axis and if a and b are lengths of semi-major and semi-minor axis respectively, then

The foci of an ellipse are located at the points (2,4) and (2,-2) . The point (4,2) lies on the ellipse. If a and b represent the lengths of the semi-major and semi-minor axes respectively, then the value of (ab)^(2) is equal to :

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

A point on the ellipse x^(2)/16 + y^(2)/9 = 1 at a distance equal to the mean of lengths of the semi - major and semi-minor axis from the centre, is

A point on the ellipse x^(2)/16 + y^(2)/9 = 1 at a distance equal to the mean of lengths of the semi - major and semi-minor axis from the centre, is

In an ellipse the length of major axis is 10 and distance between foci is 8. then length of minor axis is

If P and P denote the length of the perpendicular from a focus and the centre of an ellipse with semi - major axis of length a, respectively , on a tangent to the ellipse and r denotes the focal distance of the point , then

If P and P denote the length of the perpendicular from a focus and the centre of an ellipse with semi - major axis of length a, respectively , on a tangent to the ellipse and r denotes the focal distance of the point , then

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.