First slide

Pair of straight lines

Question

The equation ${lx}^{2} + 2 mxy + {ny}^{2} = 0$ represents a pair lines then the relation between $l, m$ is

Easy

A

$\frac{n}{m} \geq \frac{m}{l}$
B

$\frac{m}{l} \geq \frac{n}{m}$
C

$\frac{m}{l} > \frac{n}{m}$
D

$\frac{n}{m} > \frac{m}{l}$

Solution

The condition that the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ to represents a pair of lines passing through the origin is $h^{2} \geq ab$
Hence, $m^{2} \geq \ln$
It implies that $\frac{m}{l} \geq \frac{n}{m}$

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