First slide

Pair of straight lines

Question

The equation $3 x^{2} + 4 xy + {ky}^{2} = 0$ represents distinct lines then k is

Easy

A

$k < \frac{4}{3}$
B

$k > \frac{4}{3}$
C

$k \leq \frac{4}{3}$
D

$k \geq \frac{4}{3}$

Solution

The condition that the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ to represents imaginary lines is $h^{2} < ab$
Hence, $4 < 3 k$
It implies that $k > \frac{4}{3}$

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