JEE PYQ: Circle Question 39
Question 39 - 2019 (11 Jan Shift 1)
Two circles with equal radii are intersecting at the points $(0, 1)$ and $(0, -1)$. The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is:
(1) $1$
(2) $2$
(3) $2\sqrt{2}$
(4) $\sqrt{2}$
Show Answer
Answer: (2)
Solution
Let centers $O_1(a, 0)$ and $O_2(-a, 0)$ (symmetric about $y$-axis). Equal radii: $r = \sqrt{a^2 + 1}$. Tangent at $(0,1)$ to circle with center $(a,0)$: slope $= \frac{a}{1}$. This passes through $(-a, 0)$: $\frac{0-1}{-a-0} = a \Rightarrow a^2 = 1$, $a = 1$. Distance $= 2$.
BETA
