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.

Find the equation of the hyperbola with vertices are (+-6, 0) and e=5/3 . Locate its foci.

Find the equation of the hyperbola, referred to its axes as each of co-ordinates if : distance between foci is 5 and conjugate axis is 3.

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.

Find the equation of the ellipse with e=3/4 , foci on y-axis, centre at the origin, and passing through the point (6, 4).

The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci is:

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

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

Find the equation to the hyperbola whose foci, are (6,4) and (-4,4) and eccentricity is 2.

Find the equation of the hyperbola whose foaci are (0, 5) and (-2, 5) and eccentricity 3.