JEE Main 2022 · 28 Jul · Shift 1 · Mathematics Q12

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MathematicsSingle correct+4 / -1Question 12 of 90

Let C be the centre of the circle $x^2+y^2-x+2y=\dfrac{11}4$ and P be a point on the circle. A line passes through the point C, makes an angle of $\dfrac\pi4$ with the line CP and intersects the circle at the points Q and R. Then the area of the triangle PQR (in unit $^2$ ) is :

2\sqrt2

8\sin\left(\dfrac\pi8\right)

8\cos\left(\dfrac\pi8\right)

Answer and worked solution

Official answer: B

Circle has centre $\left(\frac12,-1\right)$ and radius 2.

Area. QR is a diameter (length 4) and P is at distance $2\sin\frac\pi4=\sqrt2$ from it, so the area is $\frac12\times4\times\sqrt2=2\sqrt2$ .

(B)

Topics:Equation of a circle

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JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 12