Prove tha the major axis of an ellipse is greater than its minor axis.

Prove that the major axis of an ellipse is greater than its minor aixs.

The length of the semi-major axis of an ellipse is 13 and its eccentricity is 12/13. Then the length of the semi-minor axis is

Consider the ellipse E_1, x^2/a^2+y^2/b^2=1,(a>b) . An ellipse E_2 passes through the extremities of the major axis of E_1 and has its foci at the ends of its minor axis.Consider the following property:Sum of focal distances of any point on an ellipse is equal to its major axis. Equation of E_2 is

If the length of the minor axis of an ellipse is equal to the distance between their foci, then eccntricity of the ellipse is _

The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentricity of the ellipse is

Consider an ellipse x^2/a^2+y^2/b^2=1 Let a hyperbola is having its vertices at the extremities of minor axis of an ellipse and length of major axis of an ellipse is equal to the distance between the foci of hyperbola. Let e_1 and e_2 be the eccentricities of an ellipse and hyperbola respectively. Again let A be the area of the quadrilateral formed by joining all the foci and A, be the area of the quadrilateral formed by all the directrices. The relation between e_1 and e_2 is given by

The length of latus rectum of an ellipse is equal to the length of its semi-minor axis . The ratio of lengths of its minor axis and major axis is _

If the focal distance of an end of the minor axis of an ellipse (referred to its axes as the axes of x and y , respectively) is k and the distance between its foci is 2h , then find its equation.

S , T are two foci of an ellipse and B is a one end point of minor axis . If STB be a equilateral triangle and eccentricity of the ellipse be (1)/(lambda) , then the value of lambda is _