Assertion $(A)$: If the tangent and normal to the ellipse $9x^2 + 16y^2 = 144$ at the point $P(\frac{\pi}{3})$ on it meet the major axis in $Q$ and $R$ respectively,then $QR = \frac{57}{8}$.
Reason $(R)$: If the tangent and normal to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ at the point $P(\theta)$ on it meet the major axis in $Q$ and $R$ respectively,then $QR = \left| \frac{a^2 \sin^2 \theta + b^2 \cos^2 \theta}{a \cos \theta} \right|$.

• A
  Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.
• B
  Both $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation of $(A)$.
• C
  $(A)$ is true but $(R)$ is false.
• D
  $(A)$ is false but $(R)$ is true.