1
JEE Main 2025 (Online) 7th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let P be the parabola, whose focus is $(-2,1)$ and directrix is $2 x+y+2=0$. Then the sum of the ordinates of the points on P, whose abscissa is $-$2, is

A
$\frac{5}{2}$
B
$\frac{3}{2}$
C
$\frac{3}{4}$
D
$\frac{1}{4}$
2
JEE Main 2025 (Online) 4th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
3
B
$\frac{7}{3}$
C
$\frac{8}{3}$
D
2
3
JEE Main 2025 (Online) 4th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
8
B
3
C
9
D
4
4
JEE Main 2025 (Online) 3rd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is
A
$\frac{7 \sqrt{2}}{16}$
B
$\frac{7 \sqrt{2}}{8}$
C
$\frac{7 \sqrt{2}}{2}$
D
$\frac{7 \sqrt{2}}{4}$
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