First slide

Pair of straight lines

Question

If $4 a b = 3 h^{2}$ then the ratio of the slopes of the lines represented by the equation $a x^{2} + 2 h x y + b y^{2} = 0$ will be

Moderate

A

$\sqrt{2} : 1$
B

$\sqrt{3} : 1$
C

2:1
D

1:3

Solution

$m_{1} + m_{2} = - \frac{2 h}{b} ....... (1)$
$m_{1} - m_{2} = \frac{2 \sqrt{h^{2} - a b}}{b} = \frac{2 \sqrt{h^{2} - \frac{3 h^{2}}{4}}}{b} = \frac{h}{b} ..... (2)$
Solving (1) (2), we get $m_{1} = - \frac{h}{2 b}, m_{2} = - \frac{3 h}{2 b}$

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