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

1. A Both (A) and (R) are true and (R) is the correct explanation of \((A)\).
2. B Both \((A)\) and \((R)\) are true but \((R)\) is not the correct explanation of \((A)\).
3. C (A) is true but \((\mathrm{R})\) is talse.
4. D (A) is talse but \((\mathrm{R})\) is true.