MHT-CET

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

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Q1.

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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Q2.

The equation of the circle which passes through the centre of the circle $x^2+y^2+8x+10y-7=0$ and is concentric with the circle $2x^2+2y^2-8x-12y-9=0$ is

(A)

$x^2+y^2-4x-6y+77=0$

(B)

$x^2+y^2-4x-6y-89=0$

(C)

$x^2+y^2-4x-6y+97=0$

(D)

$x^2+y^2-4x-6y-87=0$

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