JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let \(P \left( a _1, b _1\right)\) and \(Q \left( a _2, b _2\right)\) be two distinct points on a circle with center \(C (\sqrt{2}, \sqrt{3})\). Let \(O\) be the origin and \(OC\) be perpendicular to both \(CP\) and \(CQ\). If the area of the triangle \(OCP\) is \(\frac{\sqrt{35}}{2}\), then \(a _1^2+ a _2^2+ b _1^2+ b _2^2\) is equal to \(...........\).
- A \(23\)
- B \(24\)
- C \(22\)
- D \(20\)
Answer & Solution
Correct Answer
(B) \(24\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{2} \times PC \times \sqrt{5}=\frac{\sqrt{35}}{2} ; PC =\sqrt{7}\) \(a _1^2+ b _1^2+ a _2^2+ b _2^2= OP ^2+ OQ ^2\) \(=2(5+7)=24\)
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