JEE PYQ: Circle Question 40
Question 40 - 2019 (11 Jan Shift 2)
A circle cuts a chord of length $4a$ on the $x$-axis and passes through a point on the $y$-axis, distant $2b$ from the origin. Then the locus of the centre of this circle, is:
(1) a hyperbola
(2) an ellipse
(3) a straight line
(4) a parabola
Show Answer
Answer: (4)
Solution
Center $(h,k)$. Chord on $x$-axis of length $4a$: $2\sqrt{r^2 - k^2} = 4a \Rightarrow r^2 = k^2 + 4a^2$. Passes through $(0, \pm 2b)$: $h^2 + (k \mp 2b)^2 = r^2 = k^2 + 4a^2$. So $h^2 + 4b^2 \mp 4bk = 4a^2$. Locus: $x^2 \pm 4by = 4a^2 - 4b^2$, a parabola.
BETA
