First slide

Pair of straight lines

Question

The area of the square formed by the lines $6 x^{2} - 5 x y - 6 y^{2} = 0$ and $6 x^{2} - 5 x y - 6 y^{2} + x + 5 y - 1 = 0$ in sq. units is

Moderate

A

$1 / \sqrt{3}$
B

$4 / \sqrt{13}$
C

$\sqrt{13}$
D

$1 / 13$

Solution

$a = 6, 2 h = - 5, b = - 6, 2 g = 1, 2 f = 5, c = - 1$
$\frac{| c |}{2 \sqrt{h^{2} - a b}} = \frac{1}{13}$

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