For hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} - \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 1$ which of the following remains constant with change in $'\alpha '$
For hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} - \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 1$ which of the following remains constant with change in $'\alpha '$
- [IIT 2003]
- A
Abscissae of vertices
- B
Abscissae of foci
- C
Eccentricity
- D
Directrix
Similar Questions
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]
The minimum value of ${\left( {{x_1} - {x_2}} \right)^2} + {\left( {\sqrt {2 - x_1^2} - \frac{9}{{{x_2}}}} \right)^2}$ where ${x_1} \in \left( {0,\sqrt 2 } \right)$ and ${x_2} \in {R^ + }$.
The minimum value of ${\left( {{x_1} - {x_2}} \right)^2} + {\left( {\sqrt {2 - x_1^2} - \frac{9}{{{x_2}}}} \right)^2}$ where ${x_1} \in \left( {0,\sqrt 2 } \right)$ and ${x_2} \in {R^ + }$.
The eccentricity of a hyperbola passing through the points $(3, 0)$, $(3\sqrt 2 ,\;2)$ will be
The eccentricity of a hyperbola passing through the points $(3, 0)$, $(3\sqrt 2 ,\;2)$ will be
The latus-rectum of the hyperbola $16{x^2} - 9{y^2} = $ $144$, is
The latus-rectum of the hyperbola $16{x^2} - 9{y^2} = $ $144$, is
Centre of hyperbola $9{x^2} - 16{y^2} + 18x + 32y - 151 = 0$ is
Centre of hyperbola $9{x^2} - 16{y^2} + 18x + 32y - 151 = 0$ is