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 $8$
- A
$\frac{{{x^2}}}{{12}} - \frac{{{y^2}}}{4} = 1$
- B
$\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{12}} = 1$
- C
$\frac{{{x^2}}}{8} - \frac{{{y^2}}}{2} = 1$
- D
$\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1$
Similar Questions
The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$
The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$
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)
Let the foci of a hyperbola $\mathrm{H}$ coincide with the foci of the ellipse $E: \frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$ and the eccentricity of the hyperbola $\mathrm{H}$ be the reciprocal of the eccentricity of the ellipse $E$. If the length of the transverse axis of $\mathrm{H}$ is $\alpha$ and the length of its conjugate axis is $\beta$, then $3 \alpha^2+2 \beta^2$ is equal to :
Let the foci of a hyperbola $\mathrm{H}$ coincide with the foci of the ellipse $E: \frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$ and the eccentricity of the hyperbola $\mathrm{H}$ be the reciprocal of the eccentricity of the ellipse $E$. If the length of the transverse axis of $\mathrm{H}$ is $\alpha$ and the length of its conjugate axis is $\beta$, then $3 \alpha^2+2 \beta^2$ is equal to :
- [JEE MAIN 2024]
Find the equation of the hyperbola satisfying the give conditions: Foci $(0,\,\pm 13),$ the conjugate axis is of length $24.$
Find the equation of the hyperbola satisfying the give conditions: Foci $(0,\,\pm 13),$ the conjugate axis is of length $24.$
If the line $y=m x+c$ is a common tangent to the hyperbola $\frac{x^{2}}{100}-\frac{y^{2}}{64}=1$ and the circle $x^{2}+y^{2}=36,$ then which one of the following is true?
If the line $y=m x+c$ is a common tangent to the hyperbola $\frac{x^{2}}{100}-\frac{y^{2}}{64}=1$ and the circle $x^{2}+y^{2}=36,$ then which one of the following is true?
- [JEE MAIN 2020]