The equation of the circle whose entre lies on the line x-4 y=1 and which passes through the points (3,7) and (5,5) is

Step-by-step solution

Let (h, k) b the centre of the circle. It lies on the line x-4 y=1 aligned & h =1+4 k & centre (4 k +1, k ) aligned Circle passes through points (3,7) and (5,5) aligned & (4 k +1-5)^2+( k -5)^2=(4 k -2)^2+( k -7)^2 & 16 k ^2+16-32 k + k ^2+25-10 k =16 k ^2+4-16 k + k ^2+49 & -14 k aligned aligned & -42 k +41=-30 k +53 12 k =-12 k =-1 & centre (-3,-1) & Radius = (-3-5)^2+(-1-5)^2 =10 aligned Hence equation of required circle is (x+3)^2+(y+1)^2=(10)^2 i.e. x^2+y^2+6 x+2 y-90=0