WBJEE · Maths · Ellipse
The tangent at point \((a \cos \theta, b \sin \theta), 0 < \theta < \frac{\pi}{2}\), to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) meets the \(x\)-axis at \(T\) and \(y\)-axis at \(T_1\). Then the value of \(\min _{0 < \theta < \frac{\pi}{2}}(O T)\left(O T_1\right)\) is
- A \(a b\)
- B \(2 \mathrm{ab}\)
- C 0
- D 1
Answer & Solution
Correct Answer
(B) \(2 \mathrm{ab}\)
Step-by-step Solution
Detailed explanation
Hint: Tangent : \(x(b \cos \theta)+y(a \sin \theta)=a b\) \(\therefore \mathrm{OT} \cdot \mathrm{OT}_1=\frac{\mathrm{ab}}{\cos \theta \sin \theta}=\frac{2 \mathrm{ab}}{\sin 2 \theta}\)
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