·2009-04-23 04:20:27
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!
1Thanks 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)?