If the line ax by 110 meets the circle x2y2 61 at A B and P

If the line ax + by +11=0 meets the circle x^2+y^2 =61 at A, B and P(-5, 6) is on the circle such that PA= PB = 10 then |a+b|=

The line ax+by=-11 cuts the circle x²+y²=61 at A and B.

and P (-5,6) is the point on the circle such PA=PB=10

Let O be the center of the circle.

From the question , OP will be perpendicular to AB

thus the slope of line OP will be b/a since the slope of AB which is perpendicular to it is -a/b.

Equation of OP will be y=(b/a)*x

Equation of OP can also be obtained from 2 point form since O(0,0) and P(-5,6) lies over it.

Thus equation of OP will be

(y-6)/(0-6)=(x+5)/(0+5)

or, y=-6/5 x

Equating it to the other equaiton of OP that we derived we get

b/a=-6/5

b=-6/5a

or a+b =a-6/5a =-1/5*a

or |a+b|=1/5* |-a| ---i