JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the minimum area of the triangle formed by a tangent to the ellipse \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{4 a^{2}}=1\) and the co-ordinate axis is \(kab,\) then \(\mathrm{k}\) is equal to ..... .
- A \(1\)
- B \(3\)
- C \(2\)
- D \(7\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
Tangent \(\frac{x \cos \theta}{b}+\frac{y \sin \theta}{2 a}=1\) So, area \((\Delta \mathrm{OAB})=\frac{1}{2} \times \frac{\mathrm{b}}{\cos \theta} \times \frac{2 \mathrm{a}}{\sin \theta}\) \(=\frac{2 \mathrm{ab}}{\sin 2 \theta} \geq 2 \mathrm{ab}\) \(\Rightarrow \mathrm{k}=2\)
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