MHT-CET

10-1.Circle and System of Circles question bank (Mathematics)

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Q1.

The equation of the common tangent touching the circle $(x - 3)^2 + y^2 = 9$ and the parabola $y^2 = 4x$ above the $X$-axis is

(A)

$\sqrt{3}y = 3x + 1$

(B)

$\sqrt{3}y = -(x + 3)$

(C)

$\sqrt{3}y = x + 3$

(D)

$\sqrt{3}y = -(3x + 1)$

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Q2.

The angle between a pair of tangents drawn from a point $P$ to the circle ${x^2} + {y^2} + 4x - 6y + 9{\sin ^2}\alpha + 13{\cos ^2}\alpha = 0$ is $2\alpha$. The equation of the locus of the point $P$ is

(A)

${x^2} + {y^2} + 4x - 6y + 4 = 0$

(B)

${x^2} + {y^2} + 4x - 6y - 9 = 0$

(C)

${x^2} + {y^2} + 4x - 6y - 4 = 0$

(D)

${x^2} + {y^2} + 4x - 6y + 9 = 0$

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