JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Parabola

The locus of a point which divides the line segment joining the point

(0, - 1)

and a point on the parabola,

x^{2} = 4 y

, internally in the ratio

1 : 2

, is

(A) $9 x^{2} - 12 y = 8$ ✓ Correct
(B) $4 x^{2} - 3 y = 2$
(C) $x^{2} - 3 y = 2$
(D) $9 x^{2} - 3 y = 2$

Answer: (A)

Solution

Take

P (2 t, t^{2})

x^{2} = 4 y

and let

Q (h, k)

divide the segment from

(0, - 1)

P

in the ratio

1 : 2

. The section formula gives

h = \frac{2 t}{3}

and

k = \frac{t ^{2} - 2}{3}

, so

t = \frac{3 h}{2}

and

3 k = t^{2} - 2 = \frac{9 h ^{2}}{4} - 2

. Clearing fractions gives

12 k = 9 h^{2} - 8

, so the locus of

Q

9 x^{2} - 12 y = 8

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Single correct option

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