JEE PYQ: Parabola Question 12
Question 12 - 2020 (08 Jan Shift 1)
The locus of a point which divides the line segment joining the point $(0, -1)$ and a point on the parabola, $x^2 = 4y$, internally in the ratio $1 : 2$, is:
(1) $9x^2 - 12y = 8$
(2) $9x^2 - 3y = 2$
(3) $x^2 - 3y = 2$
(4) $4x^2 - 3y = 2$
Show Answer
Answer: (1)
Solution
Let $P(2t, t^2)$ on parabola and $Q(h, k)$ divides $OP$ in ratio $1:2$. $h = \frac{2t}{3}$, $k = \frac{-2+t^2}{3}$. So $3k + 2 = \left(\frac{3h}{2}\right)^2 \Rightarrow 9x^2 = 12y + 8$.
BETA
