If the tangent at a point P on the parabola y² = 3x is parallel t… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 29 January, Shift 2Conic Sections (Parabola, Ellipse, Hyperbola)

If the tangent at a point $P$ on the parabola $y^2 = 3x$ is parallel to the line $x + 2y = 1$ , and the tangents at the points $Q$ and $R$ on the ellipse $\frac{x^2}{4} + \frac{y^2}{1} = 1$ are perpendicular to the line $x - y = 2$ , then the area of the triangle $PQR$ is:

A
$\frac{9}{\sqrt{2}}$
B
$5\sqrt{3}$
C
$\frac{3}{2}\sqrt{5}$
D
$3\sqrt{5}$

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