First slide

Pair of straight lines

Question

If one of the lines given by $2 c x^{2} + 2 x y - (c^{2} - 1) y^{2} = 0 is 2 x + 3 y = 0$ then the integral value of $c$ is

Moderate

A

2
B

3
C

4
D

8

Solution

Let the slope of the other line be $m$
$\begin{array}{l} then - \frac{2}{3} \times m = \frac{2 c}{- (c^{2} - 1)} \\ and - \frac{2}{3} + m = \frac{- 2}{- (c^{2} - 1)} \\ \Rightarrow - \frac{2}{3} + \frac{3 c}{c^{2} - 1} = \frac{2}{c^{2} - 1} \\ \Rightarrow 2 c^{2} - 9 c + 4 = 0 \end{array}$

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