JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q12

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MathematicsSingle correct+4 / -1Question 12 of 90

A circle $C_1$ passes through the origin O and has diameter 4 on the positive $x$ -axis. The line $y=2x$ gives a chord OA of circle $C_1$ . Let $C_2$ be the circle with OA as a diameter. If the tangent to $C_2$ at the point A meets the $x$ -axis at P and $y$ -axis at Q, then QA : AP is equal to :

1 : 4

1 : 5

2 : 5

1 : 3

Answer and worked solution

Official answer: A

Point A. $C_1:x^2+y^2=4x$ with $y=2x$ gives $A=\left(\frac45,\frac85\right)$ .

Tangent to $C_2$ at A is perpendicular to OA: $y-\frac85=-\frac12\left(x-\frac45\right)$ . So $P=(4,0)$ and $Q=(0,2)$ .

Ratio. $QA=\sqrt{0.8}$ and $AP=\sqrt{12.8}$ , so $QA:AP=1:4$ .

(A)

Topics:Tangents and normals Equation of a circle

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JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 12