Question

Show that the line 3x + 4y + 5 = 0 and the lines (3x + 4y)² – 3(4x – 3y)² =0 form an equilateral triangle.

Answer 1

The slope of the line 3x + 4y + 5 = 0 is -3/4 Let m be the slope of one of the line making an angle of 60° with the line 3x + 4y + 5 = 0. The angle between the lines having slope m and m is 60°.

On squaring both sides, we get,

i.e. (3x + 4y)² – 3(4x – 3y)² = 0

Hence, the line 3x + 4y + 5 = 0 and the lines (3x + 4y)² – 3(4x – 3y)² form the sides of an equilateral triangle.