Conjugate axis of a hyperbola is equal to half of the distance between the foci and latus rectum is 8. Find the eccentricity of the hyperbola.

In an ellipse, the distances between its foci is 6 and minor axis is 8 . Then its eccentricity is

Find the equation of a hyperbola whose vertices lie on y-axis, centre is at the origin, the distance between the foci is 16 and eccentricity is sqrt2 .

Find the standard equation of hyperbola in each of the following cases: (i) Distance between the foci of hyperbola is 16 and its eccentricity is sqrt2. (ii) Vertices of hyperbola are (pm4,0) and foci of hyperbola are (pm6,0) . (iii) Foci of hyperbola are (0,pmsqrt(10)) and it passes through the point (2,3). (iv) Distance of one of the vertices of hyperbola from the foci are 3 and 1.

If the distance between the directrices is thrice the distance between the foci, then find eccentricity of the ellipse.

If the distance between the foci of an ellipse is equal to length of minor axis, then its eccentricity is

If, in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latus-rectum is:

Find the eccentricity of the ellipse if : the distance between the foci is equal to the length of latus-rectum.

Find the equation of the ellipse refer to its centre whose minor axis is equal to distance between the foci and latus rectum is 10.

Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 . The transverse and conjugate axes of this hyperbola coincide with the major and minor axis of the given ellipse. Also, the product of the eccentricities of the given ellipse and hyperbola is 1. Then,

Find the equation of hyperbola whose foic are (0, pm12) and length of latus rectum is 36.