Question

The line $lx+my+n=0$ is normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$; then $n^2(\frac{a^2}{l^2}-\frac{b^2}{m^2})$ is equal to

• A. $a^2-b^2$
• B. $(a^2-b^2{)}^2$
• C. $(a^2+b^2)$
• D. $(a^2+b^2{)}^2$

Answer 1

The correct option is D $(a^2+b^2{)}^2$

Equation of normal of hyperbola is $ax\cos \theta +by\cot \theta =a^2+b^2$
On comparing with $lx+my+n=0$ we get $n^2(\frac{a^2}{l^2}-\frac{b^2}{m^2})=(a^2+b^2{)}^2$