First slide

Equation of line in Straight lines

Question

Given the family of lines, $a (2 x + y + 4) + b (x - 2 y - 3) = 0$ .Among the lines of the family, the number of lines situated at a distance of $\sqrt{10}$ from the point $M (2, - 3)$ is

Moderate

A

0
B

1
C

2
D

$\infty$

Solution

The point of intersection of the two lines are (-1, -2).
Distance PM = $\sqrt{10}$
Hence the required line is one which passes through $(- 1, - 2)$ and is $⊥$ to P.M.

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