VITEEE 2019 Paper

Let (h,k) be the centre of the circle. Then k=h−1 .

Therefore, the equation of the circle is given by (x−h)2+[y−(h−1)]2=9... . (1)

Given that the circle passes through the point (7,3) and hence we get
(7−h)2+(3−(h−1))2=9
   (7−h)2+(4−h)2=9
     h2−11h+28=0

‌ which gives ‌(h−7)(h−4)=0

⇒h=4 or h=7
Therefore, the required equations of the circles are
x2+y2−8x−6y+16=0
or, x2+y2−14x−12y+76=0