The equation of the hyperbola whose conjugate axis is $5$ and the distance between the foci is $13$, is
The equation of the hyperbola whose conjugate axis is $5$ and the distance between the foci is $13$, is
- A
$25{x^2} - 144{y^2} = 900$
- B
$144{x^2} - 25{y^2} = 900$
- C
$144{x^2} + 25{y^2} = 900$
- D
$25{x^2} + 144{y^2} = 900$
Similar Questions
A tangent to a hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ intercepts a length of unity from each of the co-ordinate axes, then the point $(a, b)$ lies on the rectangular hyperbola
A tangent to a hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ intercepts a length of unity from each of the co-ordinate axes, then the point $(a, b)$ lies on the rectangular hyperbola
A hyperbola passes through the points $(3, 2)$ and $(-17, 12)$ and has its centre at origin and transverse axis is along $x$ - axis. The length of its transverse axis is
A hyperbola passes through the points $(3, 2)$ and $(-17, 12)$ and has its centre at origin and transverse axis is along $x$ - axis. The length of its transverse axis is
Product of length of the perpendiculars drawn from foci on any tangent to hyperbola ${x^2} - \frac{{{y^2}}}{4}$ = $1$ is
Product of length of the perpendiculars drawn from foci on any tangent to hyperbola ${x^2} - \frac{{{y^2}}}{4}$ = $1$ is
Let a line $L: 2 x+y=k, k\,>\,0$ be a tangent to the hyperbola $x^{2}-y^{2}=3 .$ If $L$ is also a tangent to the parabola $y^{2}=\alpha x$, then $\alpha$ is equal to :
Let a line $L: 2 x+y=k, k\,>\,0$ be a tangent to the hyperbola $x^{2}-y^{2}=3 .$ If $L$ is also a tangent to the parabola $y^{2}=\alpha x$, then $\alpha$ is equal to :
- [JEE MAIN 2021]
The locus of a point $P (h, k)$ such that the line $y = hx + k$ is tangent to $4x^2 - 3y^2 = 1$ , is a/an
The locus of a point $P (h, k)$ such that the line $y = hx + k$ is tangent to $4x^2 - 3y^2 = 1$ , is a/an