MCQ
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
    $23$
  • $24$
  • C
    $22$
  • D
    $20$

Answer

Correct option: B.
$24$
b
$\frac{1}{2} \times PC \times \sqrt{5}=\frac{\sqrt{35}}{2} ; PC =\sqrt{7}$

$a _1^2+ b _1^2+ a _2^2+ b _2^2= OP ^2+ OQ ^2$

$=2(5+7)=24$

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