JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(PQ\) be a diameter of the circle \(x ^{2}+ y ^{2}=9 .\) If \(\alpha\) and \(\beta\) are the lengths of the perpendiculars from \(P\) and \(Q\) on the straight line, \(x+y=2\) respectively, then the maximum value of \(\alpha \beta\) is
- A \(10\)
- B \(7\)
- C \(5\)
- D \(8\)
Answer & Solution
Correct Answer
(B) \(7\)
Step-by-step Solution
Detailed explanation
Let \(P(3 \cos \theta, 3 \sin \theta)\) \(Q(-3 \cos \theta,-3 \sin \theta)\) \(\Rightarrow \alpha \beta=\frac{\left|(3 \cos \theta+3 \sin \theta)^{2}-4\right|}{2}\) \(\Rightarrow \alpha \beta=\frac{5+9 \sin 2 \theta}{2} \leq 7\)
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