The radius of the larger circle lying in the first quadrant and touching the line 4 x+3 y-12=0 and the co-ordinate axes, is

Step-by-step solution

Let the equation of the circle is x^2+y^2+2 g x+2 f y+c=0 This circle touch the coordinate axes and lying in the first quadrant, then aligned g^2-c & =0 and f^2-c=0 g & = c , f= c aligned circle lies in first quadrant The centre is ( c , c ) If the line 4 x+3 y-12=0 touch the circle, then aligned & f^2+g^2-c = 4 c +3 c -12 4^2+3^2 & c+c-c = 7 c -12 5 & 5 c =7 c -12 & 2 c =12 c=36 & Radius = f^2+g^2-c = c+c-c = c =6 aligned