JEE PYQ: Circle Question 16
Question 16 - 2020 (03 Sep Shift 2)
Let the latus rectum of the parabola $y = 4x$ be the common chord to the circles $C_1$ and $C_2$ each of them having radius $2\sqrt{5}$. Then, the distance between the centres of the circles $C_1$ and $C_2$ is:
(1) $8\sqrt{5}$
(2) $8$
(3) $12$
(4) $4\sqrt{5}$
Show Answer
Answer: (2)
Solution
Latus rectum of $y^2 = 4x$: $x = 1$, length 4. Half-chord $= 2$. Distance from center to chord $= \sqrt{20 - 4} = 4$. Centers are on opposite sides, so distance $= 2 \times 4 = 8$.
BETA
