JEE PYQ: Circle Question 36
Question 36 - 2019 (10 Jan Shift 1)
If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2 + y^2 + 4x - 6y = 12$ externally at the point $(1, -1)$, then the radius of $C$ is:
(1) $2\sqrt{5}$
(2) $4$
(3) $5$
(4) $\sqrt{57}$
Show Answer
Answer: (3)
Solution
Given circle: $(x+2)^2 + (y-3)^2 = 25$, center $(-2,3)$, $r = 5$. Tangent at $(1,-1)$: common tangent. The required circle touches externally at $(1,-1)$, so its center lies on the line from $(-2,3)$ through $(1,-1)$, on the opposite side. Center at $(4,-5)$. Through $(4,0)$: $r = \sqrt{0+25} = 5$.
BETA
