JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q19

← JEE Main 2022 · 27 Jul · Shift 1

MathematicsSingle correct+4 / -1Question 19 of 90

If the circle $x^2+y^2-2gx+6y-19c=0$ , $g,c\in\mathbf R$ passes through the point $(6,1)$ and its centre lies on the line $x-2cy=8$ , then the length of intercept made by the circle on $x$ -axis is

\sqrt{11}

2\sqrt{23}

Answer and worked solution

Official answer: D

Conditions. The centre $(g,-3)$ lies on the line: $g+6c=8$ . Through $(6,1)$ : $43-12g-19c=0$ . So $c=1$ , $g=2$ .

Intercept. $2\sqrt{g^2+19}=2\sqrt{23}$ . (D)

Topics:Equation of a circle

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 19