JEE Main 2022 (28 Jul, Shift 2) Maths Q74: Conic Sections

Question

Let the hyperbola

H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

pass through the point

(2\sqrt{2},-2\sqrt{2})

. A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola ?

(1) $(2\sqrt{3},3\sqrt{2})$
(2) $(3\sqrt{3},-6\sqrt{2})$ Official answer
(3) $(\sqrt{3},-\sqrt{6})$
(4) $(3\sqrt{6},6\sqrt{2})$

Official answer

Option 2

NTA final key.

Accepted Answer

Option 2: $(3\sqrt{3},-6\sqrt{2})$

Answer

$(2\sqrt{3},3\sqrt{2})$

Answer

$(3\sqrt{3},-6\sqrt{2})$

Answer

$(\sqrt{3},-\sqrt{6})$

Answer

$(3\sqrt{6},6\sqrt{2})$

JEE Main 28 July 2022, Shift 2, Maths Q74