Engineer & Medical

Pair of Lines question bank (Maths)

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Q1.

Let $a$ and $b$ be non-zero and real numbers. Then, the equation $\left(a x^2+b y^2+c\right)\left(x^2-5 x y+6 y^2\right)=0$ represents

(A)

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

(B)

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

(C)

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

(D)

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

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Q2.

If the equation $16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0$ represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........

(A)

$4x - 3y - 1 = 0$

(B)

$4x - 3y + 1 = 0$

(C)

$8x - 6y - 1 = 0$

(D)

$8x - 6y + 1 = 0$

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