1
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Let the tangents at two points $$\mathrm{A}$$ and $$\mathrm{B}$$ on the circle $$x^{2}+\mathrm{y}^{2}-4 x+3=0$$ meet at origin $$\mathrm{O}(0,0)$$. Then the area of the triangle $$\mathrm{OAB}$$ is :

A
$$\frac{3 \sqrt{3}}{2}$$
B
$$\frac{3 \sqrt{3}}{4}$$
C
$$\frac{3}{2 \sqrt{3}}$$
D
$$\frac{3}{4 \sqrt{3}}$$
2
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

For $$\mathrm{t} \in(0,2 \pi)$$, if $$\mathrm{ABC}$$ is an equilateral triangle with vertices $$\mathrm{A}(\sin t,-\cos \mathrm{t}), \mathrm{B}(\operatorname{cost}, \sin t)$$ and $$C(a, b)$$ such that its orthocentre lies on a circle with centre $$\left(1, \frac{1}{3}\right)$$, then $$\left(a^{2}-b^{2}\right)$$ is equal to :

A
$$\frac{8}{3}$$
B
8
C
$$\frac{77}{9}$$
D
$$\frac{80}{9}$$
3
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Let $$C$$ be the centre of the circle $$x^{2}+y^{2}-x+2 y=\frac{11}{4}$$ and $$P$$ be a point on the circle. A line passes through the point $$\mathrm{C}$$, makes an angle of $$\frac{\pi}{4}$$ with the line $$\mathrm{CP}$$ and intersects the circle at the points $$Q$$ and $$R$$. Then the area of the triangle $$P Q R$$ (in unit $$^{2}$$ ) is :

A
2
B
2$$\sqrt2$$
C
$$8 \sin \left(\frac{\pi}{8}\right)$$
D
$$8 \cos \left(\frac{\pi}{8}\right)$$
4
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

The foot of the perpendicular from a point on the circle $$x^{2}+y^{2}=1, z=0$$ to the plane $$2 x+3 y+z=6$$ lies on which one of the following curves?

A
$$(6 x+5 y-12)^{2}+4(3 x+7 y-8)^{2}=1, z=6-2 x-3 y$$
B
$$(5 x+6 y-12)^{2}+4(3 x+5 y-9)^{2}=1, z=6-2 x-3 y$$
C
$$(6 x+5 y-14)^{2}+9(3 x+5 y-7)^{2}=1, z=6-2 x-3 y$$
D
$$(5 x+6 y-14)^{2}+9(3 x+7 y-8)^{2}=1, z=6-2 x-3 y$$
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