Question

The normals at the point $\theta$ and $\pi +\theta$ on $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ intersect at :

• A. the transverse axis
• B. the conjugate axis
• C. neither of the two axes
• D. on any one of them

Answer 1

The correct option is B the conjugate axis

The equation of the normal at '$\theta$' is
$ax\cos \theta +by\cot \theta =a^2+b^2$ .....(1)
$\therefore$ the equation of the normal at $\pi +\theta$ is
$-ax\cos \theta +by\cot \theta =a^2+b^2....\left(2\right)$
Solving $\left(1\right)$ and $\left(2\right)$ we get , $x=0$
$\Rightarrow$ $\left(1\right)$ and $\left(2\right)$ meet on the conjugate axis whatever may be the value of $\theta$
Hence, option 'B' is correct