If a hyperbola passes through foci of the ellipse `x^2/5^2 + y^2/3^2 = 1` and its transverse and conjugate axes coincide with the major and minor axes of the ellipse and the product of their eccentricities is 1, then the product of length of semi transverse and conjugate axes of hyperbola is...

If a hyperbola passes through the focus of the ellipse x^(2)/25+y^(2)/16=1 and its transverse and conjugate gate axis coincides with the major and minor axis of the ellipse, and product of their eccentricities is 1, then

A hyperbola passes through a focus of the ellipse (x^(2))/(169)+(y^(2))/(25)=1. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse.The product of eccentricities is 1. Then the equation of the hyperbola 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)

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 axes of the given ellipse, also the product of eccentricities of given ellipse and hyperbola is 1, then

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

" In an ellipse the major and minor axes are in the ratio " 5:3 " The eccentricity of the ellipse is "

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. Equation of ellipse is : (A) x^2/16 + y^2/9 =1 (B) x^2/25 + y^2/9 = 1 (C) x^2/25 + y^2/16 = 1 (D) none of these

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. Foci of the ellipse are (A) (+- 4, 0) (B) (+-3, 0) (C) (+-5, 0) (D) none of these

Find the lengths of the major and minor axes, coordinates of the vertices and the foci, the eccentricity and length of the latus rectum of the ellipse: 4x^(2)+9y^(2)=144.