First slide

Pair of straight lines

Question

Triangle formed by $x^{2} - 3 y^{2} = 0$ and $x = 4$ is

Moderate

A

isosceles
B

equilateral
C

right angled
D

none of these

Solution

The equations of the sides of the triangle are
$x^{2} - 3 y^{2} = 0$ and $x = 4$ or $x + \sqrt{3} y = 0, x - \sqrt{3} y = 0$ and $x = 4$
So, the coordinates of the vertices are $O (0, 0), A (4, \frac{4}{\sqrt{3}})$ and $B (4, - \frac{4}{\sqrt{3}})$
Clearly, $O A = O B = A B = \frac{8}{\sqrt{3}}$
Hence, $∆ O A B$ is equilateral.

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