If the equation of ellipse `x^2/25 + y^2/16 =1` then find the equation of hyperbola such that product of eccentircities of both curves equal to 1 and the axes of ellipse are coinciding with hyperbola and also hyperbola passes through the focii of ellipse.

The equation of the parabola whose vertex is at the centre of the ellipse x^2/25+y^2/16 = 1 and the focus coincide with the focus of the ellipse on the positive side of the major axis of the ellipse is

find the equation of the hyperbola which passes through the points of intersection of the line x+y=5 and hyperbola 2x^(2)-3y^(2)-6=0 and is also passes through (3,4).

Find the equation of the hyperbola whose eccentricity is sqrt(2) and the distance between the foci is 16, taking transverse and conjugate axes of the hyperbola as x and y-axes respectively.

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. If l and l\' be the length of semi latera recta of ellipse and hyperbola, then ll\'= (A) 144/15 (B) 256/15 (C) 225/12 (D) none of these

the equation of the ellipse passing through (2,1) having e=1/2 , is

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

The line 2x + y = 1 touches a hyperbola and passes through the point of intersection of a directrix and the x-axis. The equation of the hyperbola is

Find the equation of a hyperbola which passes through the points of intersection of the line x+y-5=0& hyperbola 2x^(2)-3y^(2)-6=0 and is also passes through (3,4)