Question

Find the combined equation of lines passing through the origin each of which making an angle of 30° with the line 3x + 2y – 11 = 0

Answer 1

The slope of the line 3x + 2y – 11 = 0 is m₁ = -3/2 .

Let m be the slope of one of the lines making an angle of 30° with the line 3x + 2y – 11 = 0. The angle between the lines having slopes m and m₁ is 30°.

On squaring both sides, we get,

∴ (2 – 3m)² = 3 (2m + 3)²

∴ 4 – 12m + 9m² = 3(4m² + 12m + 9)

∴ 4 – 12m + 9m² = 12m² + 36m + 27

3m² + 48m + 23 = 0

This is the auxiliary equation of the two lines and their joint equation is obtained by putting m =\(\frac{x}{y}\).

∴ the combined equation of the two lines is