Let the tangent drawn to the parabola … at the point … is perpendicular to the line …. Then the normal to the hyperbola … at the point … does NOT pass through the point :

Option D. Any tangent to … at (…, …)

Hyperbola

JEE Main 2022 · 26 Jul, Morning shift · Q3955

MathematicsMedium57×since 2003Q3955

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 · 26 Jul, Morning shift · Q3955

MathematicsMedium57×since 2003Q3955

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 :