If the line \( 5x - 2y - 6 = 0 \) is a tangent to the hyperbola \( 5x^2 - ky^2 = 12 \), then the equation of the normal to this hyperbola at \( (\sqrt{6}, p) \) is:
Show Hint
For hyperbola tangents and normals, differentiate implicitly and substitute known values carefully.
Step 1: Finding the normal equation
Using differentiation for the hyperbola,
\[
\frac{dy}{dx} = \frac{5x}{ky}
\]
Substituting \( x = \sqrt{6} \), solving for \( y \), and forming the normal equation gives:
\[
\sqrt{6}x - 5y = 21
\]