First slide

Equation of line in Straight lines

Question

If the line $x = a + m$ , $y = - 2$ and y=mx are concurrent , then least value of $|a|$ is

Moderate

A

0
B

$\sqrt{2}$
C

$2 \sqrt{2}$
D

2

Solution

By eliminating x,y from three equations we get –2 = m (a + m) $\Rightarrow m^{2} + a m + 2 = 0$
Since $m \in R \Rightarrow d i s \geq 0$
$∴ a^{2} - 8 \geq 0 \Rightarrow | a | \geq 2 \sqrt{2}$

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