The equation of the hyperbola whose foci are the foci of the ellipse $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1$ and the eccentricity is $2$, is
The equation of the hyperbola whose foci are the foci of the ellipse $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1$ and the eccentricity is $2$, is
- A
$\frac{{{x^2}}}{4} + \frac{{{y^2}}}{{12}} = 1$
- B
$\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{12}} = 1$
- C
$\frac{{{x^2}}}{{12}} + \frac{{{y^2}}}{4} = 1$
- D
$\frac{{{x^2}}}{{12}} - \frac{{{y^2}}}{4} = 1$
Similar Questions
The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is equal to (where $e$ is the eccentricity of the hyperbola)
The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is equal to (where $e$ is the eccentricity of the hyperbola)
The equation to the hyperbola having its eccentricity $2$ and the distance between its foci is $8$
The equation to the hyperbola having its eccentricity $2$ and the distance between its foci is $8$
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If the eccentricities of the hyperbolas $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ and $\frac{{{y^2}}}{{{b^2}}} - \frac{{{x^2}}}{{{a^2}}} = 1$ be e and ${e_1}$, then $\frac{1}{{{e^2}}} + \frac{1}{{e_1^2}} = $
If the foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{{b^2}}} = 1$ coincide with the foci of the hyperbola $\frac{{{x^2}}}{{144}} - \frac{{{y^2}}}{{81}} = \frac{1}{{25}},$ then $b^2$ is equal to
If the foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{{b^2}}} = 1$ coincide with the foci of the hyperbola $\frac{{{x^2}}}{{144}} - \frac{{{y^2}}}{{81}} = \frac{1}{{25}},$ then $b^2$ is equal to
- [AIEEE 2012]
The auxiliary equation of circle of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, is
The auxiliary equation of circle of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, is