Let the tangent drawn to the parabola $y ^{2}=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x$ $+2 y=5$. Then the normal to the hyperbola $\frac{x^{2}}{\alpha^{2}}-\frac{y^{2}}{\beta^{2}}=1$ at the point $(\alpha+4, \beta+4)$ does $NOT$ pass through the point.
Let the tangent drawn to the parabola $y ^{2}=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x$ $+2 y=5$. Then the normal to the hyperbola $\frac{x^{2}}{\alpha^{2}}-\frac{y^{2}}{\beta^{2}}=1$ at the point $(\alpha+4, \beta+4)$ does $NOT$ pass through the point.
- [JEE MAIN 2022]
- A
$(25,10)$
- B
$(20,12)$
- C
$(30,8)$
- D
$(15,13)$
Similar Questions
Latus rectum of the conic satisfying the differential equation, $ x dy + y dx = 0$ and passing through the point $ (2, 8) $ is :
Latus rectum of the conic satisfying the differential equation, $ x dy + y dx = 0$ and passing through the point $ (2, 8) $ is :
Eccentricity of the rectangular hyperbola $\int_0^1 {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^3}}}} \right)} \;dx$ is
Eccentricity of the rectangular hyperbola $\int_0^1 {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^3}}}} \right)} \;dx$ is
The equation of the director circle of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{4} = 1$ is given by
The equation of the director circle of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{4} = 1$ is given by
The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$
The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $16 x^{2}-9 y^{2}=576$
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $16 x^{2}-9 y^{2}=576$