If Q is the inverse point of the point P (2,3) with respect to the circle x^2+y^2-2 x-2 y+1=0 , then the circle with PQ as diameter is

Step-by-step solution

Let the co-ordinate of the point Q is (h, k) . Equation of line O P : (y-3)= 2 1 (x-1) 2 x-y=1 ...(1) (h, k) is on the line O P 2 h-k=1 k=2 h-1 So, co-ordinate of P is (h, 2 h-1) . Also, O P O Q=r^2 aligned & 1+4 O Q^ =r^2 O Q= 1 5 & (h-1)^2+(2 h-1-1)^2 = 1 5 aligned aligned & 25 h^2-50 h+24=0 & h= 6 5 , 4 5 aligned Let h= 6 5 . Then k=2 6 5 -1= 7 5 Then Q= ( 6 5 , 7 5 ) . Eqn. of line with P Q as diameter is aligned & (x-2) (x- 6 5 )+(y-3) (y- 7 5 )=0 & (x-2)(5 x-6)+(5 y-7)(y-3)=0 & 5 x^2+5 y^2-6 x-22 y+33=0 . ali