First slide

Pair of straight lines

Question

If O, A, B are vertices of triangle whose sides are given by ${(5 x + 12 y)}^{2} - 3 {(12 x - 5 y)}^{2} = 0.5 x + 12 y - 78 = 0$ then AB=

Moderate

A

$\sqrt{3}$
B

$2 \sqrt{3}$
C

$3 \sqrt{3}$
D

$4 \sqrt{3}$

Solution

$l = 5, m = 12, n = - 78$
a side of equilateral triangle $\frac{\sqrt{3}}{4} a^{2} = \frac{n^{2}}{\sqrt{3} (l^{2} + m^{2})}$

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