Consider circles C 1 & C 2 touching both the axes and passing through 4,4 , then the product of radii of these circles is

Question

Consider circles C 1 & C 2 touching both the axes and passing through 4,4 , then the product of radii of these circles is,

MARKS App · Accepted Answer

Since circle touches both the axes and passes through

(4,4)

, it lies in the first quadrant, so its equation is

{(x - r)}^{2} + {(y - r)}^{2} = r^{2}

(4,4)

lies on it hence

r^{2} - 16 r + 32 = 0

Hence, the product of roots (radii)

= 32