Question

If the line \( lx + my - n = 0 \) will be a normal to the hyperbola, then \( \frac{a^2}{l^2} + \frac{b^2}{m^2} = k \), where \( k \) is equal to?

• A. \( \frac{n}{3} \)
• B. \( \frac{a^2}{b^2} \)
• C. \( \frac{n^2}{3} \)
• D. None of these

Hint:

For normal lines to conic sections, the relationships between the coefficients and the parameters of the conic can simplify the equation.

Answer 1

The Correct Option is B

For the equation of the normal to the hyperbola, the relationship between the coefficients of the normal equation and the hyperbola’s semi-axes leads to \( \frac{a^2}{l^2} + \frac{b^2}{m^2} = \frac{a^2}{b^2} \).