1
JEE Main 2025 (Online) 22nd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the parabola $y=x^2+\mathrm{p} x-3$, meet the coordinate axes at the points $\mathrm{P}, \mathrm{Q}$ and R . If the circle C with centre at $(-1,-1)$ passes through the points $P, Q$ and $R$, then the area of $\triangle P Q R$ is :

A
4
B
6
C
5
D
7
2
JEE Main 2024 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$C$$ be the circle of minimum area touching the parabola $$y=6-x^2$$ and the lines $$y=\sqrt{3}|x|$$. Then, which one of the following points lies on the circle $$C$$ ?

A
$$(1,2)$$
B
$$(2,2)$$
C
$$(1,1)$$
D
$$(2,4)$$
3
JEE Main 2024 (Online) 4th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$P Q$$ be a chord of the parabola $$y^2=12 x$$ and the midpoint of $$P Q$$ be at $$(4,1)$$. Then, which of the following point lies on the line passing through the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ ?

A
$$(3,-3)$$
B
$$\left(\frac{1}{2},-20\right)$$
C
$$(2,-9)$$
D
$$\left(\frac{3}{2},-16\right)$$
4
JEE Main 2024 (Online) 27th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the shortest distance of the parabola $y^2=4 x$ from the centre of the circle $x^2+y^2-4 x-16 y+64=0$ is $\mathrm{d}$, then $\mathrm{d}^2$ is equal to :
A
16
B
24
C
20
D
36
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