Question

The obtuse angle bisector of the lines x – 2y + 4 = 0 and 4x – 3y + 2 = 0 is

(a) x(4 – √5) + y(2√5 – 3) + (2 + 4√5) = 0

(b) x(4 – √5) + y(2√5 – 3) + (2 – 4√5) = 0

(c) x(4 + √5) + y(2√5 – 3) + (2 + 4√5) = 0

(d) x(4 + √5) + y(2√5 + 3) + (2 + 4√5) = 0

Answer 1

The correct option (b) x(4 – √5) + y(2√5 – 3) + (2 – 4√5) = 0

Explanation:

lines: x – 2y + 4 = 0 and 4x – 3y + 2 = 0

obtuse angle bisector is

[(x – 2y + 4)/√{1² + (– 2)²}] = [(4x – 3y + 2)/√{4² + (– 3)²}]

∴ [(x – 2y + 4)/√5] = [(4x – 3y + 2)/5]

∴ 5x – 10y + 20 = 4√5x – 3√5y + 2√5

∴ x(4√5 – 5) – y(3√5 – 10) + 2√5 – 20 = 0

∴ x(4 – √5) + y(√5 ∙ 2 – 3) + (2 – 4√5) = 0

∴ x(4 – √5) + y(2√5 – 3) + (2 – 4√5) = 0