If sum of reciprocal of radii of all the circles which touches all the lines represented by the equation x^2 y-2 x y^2-4 x y=0 is k (1+ 2 p ) , where k, p N , then find the value of (k+p)

Step-by-step solution

gathered x^2 y-2 x y^2-4 x y=0 x y(x-2 y-4)=0 r= s = 1 2 2 4 3+ 5 = 4 3+ 5 Required sum = 2 r = 2(3+ 5 ) 4 = 6+2 5 4 = ( 5 +1)^2 4 gathered aligned & =4 ^2 5 =2 (1+ 2 p ) k (1+ 2 p ) & k+p=2+5=7 & aligned