1. Tardigrade
  2. Question
  3. Mathematics
  4. Let P(3 sec θ, 2 tan θ) and Q(3 sec φ, 2 tan φ) where θ+φ=(π/2), be two distinct points on the hyperbola (x2/9)-(y2/4)=1. Then the ordinate of point of intersection of the normals at P and Q is

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Q. Let $P(3 \sec \theta, 2 \tan \theta)$ and $Q(3 \sec \phi, 2 \tan \phi)$ where $\theta+\phi=\frac{\pi}{2}$, be two distinct points on the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$. Then the ordinate of point of intersection of the normals at $P$ and $Q$ is

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Solution:

We have,
$3 x \cos \theta+2 y \cot \theta=13 $.....(1)
$3 x \sin \theta+2 y \tan \theta=13$ ....(2)
$\therefore$ On solving (1) and (2), we get
$y=\frac{-13}{2}$