First slide

Pair of straight lines

Question

The triangle formed by the pair of lines $11 x^{2} + 16 xy - y^{2} = 0$ and $x - 2 y + 13 = 0$ is

Moderate

A

Equilateral
B

Isosceles
C

Right angled
D

Scalane

Solution

The combined equation of pair of lines passing through the origin and forming equilateral triangle with the line $ax + by + c = 0$ is ${(ax + by)}^{2} - 3 {(bx - ay)}^{2} = 0$
The combined equation of pair of lines passing through the origin and forming equilateral triangle with the line $x - 2 y + 13 = 0$ is ${(x - 2 y)}^{2} - 3 {(2 x + y)}^{2} = 0$
Simplifying the above equation, we get $11 x^{2} + 16 xy - y^{2} = 0$
Therefore, the triangle formed by the given lines is equilateral triangle.

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