Radical Axis of Circles

Let 2 circles S1=0 and S2=0 intersect at point A & B. L1=0 is the line joining A & B where S1=x2 + y2 + 2ax + 2by -5 = 0 and S2:(x+1)2 + (y+2)2 = 9. Let AB subtend an angle C at origin. Angle subtended by S1=0 and S2=0 at p(3,4) is A & B respectively.

If equn. of L1: 3x + 4y = 7, then value of (4a +b) is equal to what?

If A=60°, then (a,b) lies on a circle whose radius is what?

Hites: Equation of the line L1 is given by S1-S2
also The angle 90 degree is substended by the diagonal of the square!

Thanks for the answer. Now,

Let 2 circles S1=0 and S2=0 intersect at point A & B. L1=0 is the line joining A & B where S1=x2 + y2 + 2ax + 2by -5 = 0 and S2:(x+1)2 + (y+2)2 = 9. Let AB subtend an angle C at origin. Angle subtended by S1=0 and S2=0 at p(3,4) is A’ & B’ respectively.

If A’=60°, then (a,b) lies on a circle whose radius is what?

My method:

Using T² = (S)(S1), we get the equn. of pair of tangents from p to S1 in the form:A"x² + 2Hxy + B"y² = 0.
Then can we use tanθ = (2√(H² - A"B"))/(A" + B") to find the locus of (a,b)?