Question

The liens y = mx bisects the angle between the lines

ax² + 2hxy + by² = 0 if –

• A. h (1 + m²) = m (a + b)
• B. h (1 – m²) = m (a – b)
• C. h (1 + m²) = m (a – b)
• D. None of these

Answer 1

Answer: (B)

h (1 – m²) = m (a – b)

Answer 2

Equation of pair of bisectors of angles between lines

ax² + 2hxy + by² = 0 is

$\frac{x^{2} - y^{2}}{xy}$ = $\frac{a - b}{h}$ Ž h(x² – y²) = (a – b)xy … (1)

But y = mx is one of these lines, then it will satisfy it. Substituting y = mx in (1)

h (x² – m²x²) = (a – b)x. mx

Dividing by x², h (1 – m²) = m(a – b).