If the foci of `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` coincide with the foci of `(x^(2))/(25)+(y^(2))/(9)=1` and the eccentricity of the hyperbola is 2, then

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

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.

If the foci of (x^(2))/(16)+(y^(2))/(4)=1 and (x^(2))/(a^(2))-(y^(2))/(3)=1 coincide, the value of a is

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then,

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

If e_(1) is the eccentricity of the ellipse (x^(2))/(25)+(y^(2))/9=1 and if e_(2) is the eccentricity of the hyperbola 9x^(2)-16y^(2)=144 , then e_(1)e_(2) is. . . . .

Statement 1:If a point (x_1,y_1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1 , shown in the figure, then (x^2)/(a^2)-(y^2)/(b^2)<0 Statement 2 : If P(x_1,y_1) lies outside the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then (x_1^ 2)/(a^2)-(y_1 ^2)/(b^2)<1

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