JEE PYQ: Circle Question 3
Question 3 - 2021 (17 Mar Shift 1)
The line $2x - y + 1 = 0$ is a tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x - 2y = 4$. Then, the radius of the circle is:
(1) $3\sqrt{5}$
(2) $5\sqrt{3}$
(3) $5\sqrt{4}$
(4) $4\sqrt{5}$
Show Answer
Answer: (1)
Solution
Tangent at $(2,5)$: slope $= 2$. Radius is perpendicular: slope $= -1/2$. Line through $(2,5)$: $y-5 = -\frac{1}{2}(x-2) \Rightarrow x + 2y = 12$. Center lies on $x - 2y = 4$ and $x + 2y = 12$: center $(8, 2)$. Radius $= \sqrt{36 + 9} = 3\sqrt{5}$.
BETA
