A point P moves in X-Y plane such that sum of square of its distances from two intersecting lines is $x^2-3y^2=0$  is always 12. Let the locus of point P be $C_1\equiv \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a,b>0$  Consider another curve  $C_2\equiv b{x}^2-b^{2}a=a^{2}b-a{y}^2$. A tangent to the curve $C_1$ at point P meets the curve $C_2$ at A & B. The tangents at A & B to the curve $C_2$ meets at point R. On the basis of above information answer the following questions: