If the four distinct points (4,6),(-1,5),(0,0) and ( k , 3 k ) lie on a circle of radius r , then 10 k + r ^2 is equal to

Step-by-step solution

m ₁ ~m ₂=-1 so right angle equation circle is aligned & (x-4)(x-0)+(y-6)(y-0)=0 & x^2+y^2-4 x-6 y=0 aligned ( k , 3 k ) lies on it so aligned & k ^2+9 k ^2-4 k -18 k =0 & 10 k ^2-22 k =0 aligned k =0, 11 5 k =0 is not possible so k = 11 5 also r = 4+9 = 13 so 10 k + r ^2=10 11 5 +( 13 )^2=35