Find the equation of a hyperbola referred to its axes as axes of co-ordinates, if the distance between the foci is 16 and eccentricity is `sqrt(2)`.

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 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 equation of the ellipse referred to its axes as the axes of co-ordinates : which passes through the points ( - 2, 1) and eccentricity = sqrt (2/5)

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : whose latus-rectum is 5 and eccentricity 2/3 .

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : whose major axis = 8 and eccentricity = 1/2 .

Find the equation of the hyperbola, referred to its axes as each of co-ordinates if : conjugate axis is 5 and passes through the point (1, -2).

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : whose major axis =6 and minor axis = 4 .

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 ellipse referred to its axes as the axes of co-ordinates : whose foci are (2, 0), (-2, 0) and latus-rectum is 6.

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.