If the eccentricity is zero, prove that the ellipse becomes a circle.

Obtain the equation of the ellipse whose latus rectum is 5 and whose eccentricity is 2/3 , the axes of the ellipse being the axes of coordinates.

Consider an ellipse having its foci at A(z_1)a n dB(z_2) in the Argand plane. If the eccentricity of the ellipse be e and it is known that origin is an interior point of the ellipse, then prove that e in (0,(|z_1-z_2|)/(|z_1|+|z_2|))

Let the major axis of a standard ellipse equals the transverse axis of a standard hyperbola and their director circles have radius equal to 2R and R respectively. If e_(1) and e_(2) , are the eccentricities of the ellipse and hyperbola then the correct relation is

If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricity is 5/6 then the equation of the ellipse is

The focus of an ellipse is (-1, -1) and the corresponding directrix is x - y + 3 = 0 . If the eccentricity of the ellipse is 1/2, then the coordinates of the centre of the ellipse, are

A circle of maximum area is inscribed in an ellipse. If p is the probability that a point within the ellipse chosen at random lies outside the circle, then the eccentricity of the ellipse is

Let S and S'' be the fociof the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is i.e. P is a variable point on the ellipse. Consider the locus the incenter of DeltaPSS'' The eccentricity of the locus oc the P is (a) ellipse (b) hyperbola (a) parabola (d) circle

Suppose an ellipse and a hyperbola have the same pair of foci on the x -axis with centres at the origin and they intersect at (2,2) . If the eccentricity of the ellipse is (1)/(2) , then the eccentricity of the hyperbola, is

If the eccentricity of an ellipse is 5/8 and the distance between its foci is 10 , then find the latusrectum of the ellipse.

If the eccentricity of an ellipse is 5/8 and the distance between its foci is 10 , then find the latusrectum of the ellipse.