Question

If (a + 3b)(3a + b) = 4h², then the angle between the lines represented by ax² + 2hxy + by² = 0 is ______ 

Options

• 30°

• 45°

• 60°

• `tan^-1  1/2`

Answer 1

If (a + 3b)(3a + b) = 4h², then the angle between the lines represented by ax² + 2hxy + by² = 0 is 60°.

Explanation:

Given equation of pair of lines is

ax² + 2hxy + by² = 0

∴ A = a, H = h, B = b

`tantheta = |(2sqrt(H^2 - AB))/(A + B)|`

= `|(sqrt(4h^2 - 4ab))/(a + b)|`

= `|sqrt(3a^2 + 3b^2 + 10ab - 4ab)/(a + b)|` .........`[∵ 3a^2 + 3b^2 + 10ab = 4h^2]`

∴ `tantheta = |(sqrt(3(a + b)^2))/(a + b)|`

⇒ θ = `tan^-1(sqrt3)`

= 60°