Properties of Orthogonality of Two Circles

Q.

Find the equation of the circle orthogonal to the circles $x^2+y^2+3x-5y+6=0and4x^2+4y2-28x+29=0$ and whose center lies on the line 3x + 4y + 1 = 0.

1. $x^2+y^2+\frac{y}{4}-\frac{29}{4}=0$

2. $2x^2+2y^2+y-29=0$

3. $8x^2+8y^2+2y-29=0$

4. $4x^2+4y^2+2y-29=0$

Q. A circle $C_1$ passes through the origin and has its centre on the line $y=x$. Let $C_1$ cuts $C_2:x^2+y^2-4x-6y+10=0$ orthogonally. If the radius of $C_1$ is $r$, then the value of $8r^2$ is