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,

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 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 auxiliary circle of the ellipse x^(2)/25 + y^(2)/16 = 1

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

The eccentricity of ellipse (x^(2))/(25)+(y^(2))/(9)=1 is ……………. .

The foci a hyperbola coincides with the foci of the ellispe x^(2)/25 + y^(2)/9 = 1 . Find the equation of the hyperbola if its eccentricity is 2.

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If e_1a n de_2 are the eccentricities of the ellipse and the hyperbola, respectively, then prove that 1/(e1 2)+1/(e2 2)=2 .

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

Let S and S' be the fociof the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is e. P is a variable point on the ellipse. Consider the locus the incenter of DeltaPSS' The eccentricity of the locus of the P is

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 and the hyperbola (x^(2))/(25)-(y^(2))/(16) =1 have in common

If the foci of the ellipse x^(2)/16 + y^(2)/b^(2) =1 and the hyperbola x^(2)/144 - y^(2)/81 = 1/25 coincide then b^(2) is