First slide

Equation of line in Straight lines

Question

The line parallel to $x -$ axis passing through the intersection of the lines $a x + 2 b y + 3 b = 0$ and $b x - 2 a y - 3 a = 0$ where $(a, b) \neq (0, 0)$ is

Moderate

A

above $x -$ axis at a distance $3 / 2$ from it.
B

above $x -$ axis at a distance $2 / 3$ from it.
C

below $x -$ axis at a distance 3/2 from it.
D

below $x -$ axis at a distance $2 / 3$ from it.

Solution

Eliminating $x$ , we get
$(2 b^{2} + 2 a^{2}) y + 3 b^{2} + 3 a^{2} = 0$
$\Rightarrow y = - 3 / 2$ which is the required line and hence below x-axis at a distance $3 / 2$ from it.

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