The foci of the hyperbola $9{x^2} - 16{y^2} = 144$ are
The foci of the hyperbola $9{x^2} - 16{y^2} = 144$ are
- A
$( \pm 4,\;0)$
- B
$(0,\; \pm 4)$
- C
$( \pm 5,\;0)$
- D
$(0,\; \pm 5)$
Similar Questions
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
Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2 x-y=1$. The points of contacts of the tangents on the hyperbola are
$(A)$ $\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ $(B)$ $\left(-\frac{9}{2 \sqrt{2}},-\frac{1}{\sqrt{2}}\right)$
$(C)$ $(3 \sqrt{3},-2 \sqrt{2})$ $(D)$ $(-3 \sqrt{3}, 2 \sqrt{2})$
Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2 x-y=1$. The points of contacts of the tangents on the hyperbola are
$(A)$ $\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ $(B)$ $\left(-\frac{9}{2 \sqrt{2}},-\frac{1}{\sqrt{2}}\right)$
$(C)$ $(3 \sqrt{3},-2 \sqrt{2})$ $(D)$ $(-3 \sqrt{3}, 2 \sqrt{2})$
- [IIT 2012]
The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$
The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$
If for a hyperbola the ratio of length of conjugate Axis to the length of transverse axis is $3 : 2$ then the ratio of distance between the focii to the distance between the two directrices is
If for a hyperbola the ratio of length of conjugate Axis to the length of transverse axis is $3 : 2$ then the ratio of distance between the focii to the distance between the two directrices is
The normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1$ at the point $(8,3 \sqrt{3})$ on it passes through the point
The normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1$ at the point $(8,3 \sqrt{3})$ on it passes through the point
- [JEE MAIN 2022]