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.

Let $a$ and $b$ be two non-zero real numbers. The equation $(ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0$ represents:

(A)

$A$ circle and an ellipse,when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$.

(B)

Two straight lines and a hyperbola,when $a$ and $b$ are of the same sign and $c$ is of opposite sign to $a$.

(C)

Four straight lines,when $c = 0$ and $a, b$ are of the same sign.

(D)

Two straight lines and a circle,when $a = b$ and $c$ is of sign opposite to that of $a$.

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