JEE PYQ: Circle Question 29
Question 29 - 2019 (10 Apr Shift 1)
The line $x = y$ touches a circle at the point $(1, 1)$. If the circle also passes through the point $(1, -3)$, then its radius is:
(1) $3$
(2) $2\sqrt{2}$
(3) $2$
(4) $3\sqrt{2}$
Show Answer
Answer: (2)
Solution
Center lies on normal to $x = y$ at $(1,1)$: line $y - 1 = -(x-1)$, i.e., $x + y = 2$. Center $= (k, 2-k)$. Equal distances to $(1,1)$ and $(1,-3)$: $(k-1)^2 + (1-k)^2 = (k-1)^2 + (5-k)^2$. $2(k-1)^2 = (k-1)^2 + (5-k)^2$. Solving: $k = -1$. Center $(-1, 3)$, radius $= \sqrt{4+4} = 2\sqrt{2}$.
BETA
