Parabola

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JEE Main 2021 (Online) 31st August Morning ShiftQuestion 1

The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$-axis at a distance $R$ and $S$ ($>R$) respectively from the origin, is :

Parabola

$2(S+R)$$2(S-R)$$4(S+R)$$4(S-R)$

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 2

The tangents, to the parabola $y^{2}=2-x$ at the points of its intersection with the line $y=x-2$, intersect at the point

Parabola

$\left(-\frac{1}{2},2\right)$$\left(2,-\frac{1}{2}\right)$$(2,0)$$\left(2,-\frac{3}{2}\right)$

JEE Main 2021 (Online) 25th July Morning ShiftQuestion 3

Let a parabola $P$ be such that its vertex and focus lie on the positive $x$-axis at a distance $2$ and $4$ units from the origin, respectively. If tangents are drawn from $O(0,0)$ to the parabola $P$ which meet $P$ at $S$ and $R$, then the area (in sq. units) of $\triangle SOR$ is equal to :

Parabola

$16$$16\sqrt{2}$$8\sqrt{2}$$32$

JEE Main 2021 (Online) 4th August Morning ShiftQuestion 4

The locus of the mid-points of the perpendiculars to the directrix of the parabola, $y^{2}=2x$ from points on it, is

Parabola

$y^{2}=4x-1$$y^{2}=4x+1$$y^{2}=8x+2$$y^{2}=2x+\frac{1}{2}$

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 5

Let $O$ be the vertex of the parabola $y^{2}=4x$ and its chords $OP$ and $OQ$ are perpendicular to each other. If the locus of the mid-point of the line segment $PQ$ is a conic $C$, then the length of its latus rectum is :

Parabola

$1$$2$$4$$8$