The foci of a hyperbola coincide with the foci of the ellipse `(x^(2))/(25)+(y^(2))/(9)=1`, find the equation of hyperbola if ecentricity is 2.

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,

the equation of the circle passing through the foci of the ellipse (x^(2))/(16)+(y^(2))/(9)=1 and having centre at (0,3) is

If foci of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 coincide with the foci of (x^(2))/(25)+(y^(2))/(16)=1 and eccentricity of the hyperbola is 3. then

The foci of the ellipse 25(x+1)^2 + 9(y+2)^2 = 225 , are at :

Find the lengths of major and minor axes,the coordinate of foci, vertices and the eccentricity of the ellipse 3x^(2)+2y^(2)=6 . Also the equation of the directries.

Find the angle between the asymptotes of the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 .

The equation of a hyperbola conjugate to the hyperbola x^(2)+3xy+2y^(2)+2x+3y=0 is

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.