First slide

Pair of straight lines

Question

The area of the equilateral triangle formed by the pair of lines passing through the origin with the line $3 x + 4 y - 5 = 0$

Moderate

A

$\frac{1}{\sqrt{3}}$
B

1
C

$\frac{5}{\sqrt{3}}$
D

2

Solution

The area of the equilateral triangle formed by the lines $ax + by + c = 0$ and the pair of lines passing through the origin is $\frac{c^{2}}{\sqrt{3} (a^{2} + b^{2})}$
Here, $a = 3, b = 4, c = - 5$
The area of the triangle is $\frac{(- 5)^{2}}{\sqrt{3} (9 + 16)} = \frac{1}{\sqrt{3}} square units$

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