JEE Main 2023 (Online) 30th January Evening Shift | Parabola Question 23 | Mathematics

Let $A$ be a point on the $x$-axis. Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16 x$. If one of these tangents touches the two curves at $Q$ and $R$, then $(Q R)^2$ is equal to :

JEE Main 2023 (Online) 30th January Evening Shift

MCQ (Single Correct Answer)

-1

The parabolas : $a x^2+2 b x+c y=0$ and $d x^2+2 e x+f y=0$ intersect on the line $y=1$. If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in G.P., then :

$\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in A.P.

$\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in G.P.

$d, e, f$ are in A.P.

$d, e, f$ are in G.P.

JEE Main 2023 (Online) 30th January Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $$\mathrm{P}(\mathrm{h}, \mathrm{k})$$ be a point on the parabola $$x=4 y^{2}$$, which is nearest to the point $$\mathrm{Q}(0,33)$$, then the distance of $$\mathrm{P}$$ from the directrix of the parabola $$\quad y^{2}=4(x+y)$$ is equal to :

JEE Main 2023 (Online) 29th January Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

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 :

$$\frac{9}{\sqrt5}$$

$$3\sqrt5$$

$$5\sqrt3$$

$$\frac{3}{2}\sqrt5$$

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