JEE Main 2025 (Online) 4th April Evening Shift | Parabola Question 3 | Mathematics

A line passing through the point $\mathrm{A}(-2,0)$, touches the parabola $\mathrm{P}: y^2=x-2$ at the point $B$ in the first quadrant. The area, of the region bounded by the line $A B$, parabola $P$ and the $x$-axis, is :

$\frac{7}{3}$

$\frac{8}{3}$

JEE Main 2025 (Online) 4th April Evening Shift

MCQ (Single Correct Answer)

-1

The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at distances $\sqrt{2}$ and $2 \sqrt{2}$ units from the origin, respectively. If the point $(1, k)$ lies on the parabola, then a possible value of k is :

JEE Main 2025 (Online) 3rd April Morning Shift

MCQ (Single Correct Answer)

-1

The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is

$\frac{7 \sqrt{2}}{16}$

$\frac{7 \sqrt{2}}{8}$

$\frac{7 \sqrt{2}}{2}$

$\frac{7 \sqrt{2}}{4}$

JEE Main 2025 (Online) 2nd April Evening Shift

MCQ (Single Correct Answer)

-1

Let the point P of the focal chord PQ of the parabola $y^2=16 x$ be $(1,-4)$. If the focus of the parabola divides the chord $P Q$ in the ratio $m: n, \operatorname{gcd}(m, n)=1$, then $m^2+n^2$ is equal to :