Let P(a_1, b_1) and Q(a_2, b_2) be two distinct points on a circle with center C(√ 2, √ 3 ). Let O be the origin and OC be perpendicular to both CP…

Let $\displaystyle P\left(a_1, b_1\right)$ and $\displaystyle Q\left(a_2, b_2\right)$ be two distinct points on a circle with center $\displaystyle C(\sqrt{2}, \sqrt{3})$. Let O be the origin and OC be perpendicular to both CP and CQ . If the area of the triangle OCP is $\displaystyle \frac{\sqrt{35}}{2}$, then $\displaystyle a_1^2+a_2^2+b_1^2+b_2^2$ is equal to $\displaystyle \_\_\_\_$.