The center of an ellipse is `C` and `P N` is any ordinate. Point `A ,A '` are the endpoints of the major axis. Then find the value of `(P N^2)/((A N)dotA'Ndot)`

If ^ n P_5 = 20 ^nP_3 find the value of n

If C is the center of the ellipse 9x^2+16 y^2=144 and S is a focus, then find the ratio of C S to the semi-major axis.

The lengths of the major and minor axes of an ellipse are 2 a and 2b and N is the foot of the perpendicular drawn from a point P of the ellipse on the major axis . Show that (PN^(2))/(overline(AN)*overline(A'N))=(b^(2))/(a^(2)) where A and A' are the two vertices of the ellipse.

If the numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n.

If the area of the triangle included between the axes and any tangent to the curve x^n y=a^n is constant, then find the value of ndot

The sum of n terms of an A.P is n^2 .Find the common difference.

If the sub-normal at any point on y=a^(1-n)x^n is of constant length, then find the value of ndot

P is the point on the ellipse is x^2/16+y^2/9=1 and Q is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

A circle has the same center as an ellipse and passes through the foci F_1a n dF_2 of the ellipse, such that the two curves intersect at four points. Let P be any one of their point of intersection. If the major axis of the ellipse is 17 and the area of triangle P F_1F_2 is 30, then the distance between the foci is

The first and second terms of a G.P. are x^(-4) and x^n , respectively. If x^(52) is the 8th term, then find the value of ndot