If (5, 12) and (24, 7) are the foci of an ellipse passing through the origin, then find the eccentricity of the ellipse.

If (5,12)a n d(24 ,7) are the foci of a hyperbola passing through the origin, then e=(sqrt(386))/(12) (b) e=(sqrt(386))/(13) L R=(121)/6 (d) L R=(121)/3

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

if vertices of an ellipse are (-4,1),(6,1) and x-2y=2 is focal chord then the eccentricity of the ellipse is

If the foci of an ellipse are (0,+-1) and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.

P and Q are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is

If the area of a square circumscribing an ellipse is 10 square units and maximum distance of a normal from the centre of the ellipse is 1 unit, than find the eccentricity of ellipse

The ratio of the area of triangle inscribed in ellipse x^2/a^2+y^2/b^2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse.

Find the center, foci, the length of the axes, and the eccentricity of the ellipse 2x^2+3y^2-4x-12 y+13=0

If alphaa n dbeta are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is (sinalpha+sinbeta)/("sin"(alpha+beta))