Question

The angle between the lines represented by the equation ax² + xy + by² = 0 will be 45°, if ______ 

पर्याय

• a = 1, b = 6

• a = 1, b = -6

• a = 6, b = 1

• a = 1, b = 1

Answer 1

The angle between the lines represented by the equation ax² + xy + by² = 0 will be 45°, if a = 1, b = -6.

Explanation:

Given the equation of pair of lines is ax² + xy + by² = 0

∴ A = a, H = `1/2`, B = b

Now, θ = 45° ⇒ tan θ = 1

∴ tan45° = `|(2sqrt(1/4 - ab))/(a + b)|`

⇒ (a + b)² = (1 - 4ab)

⇒ a² + b² + 6ab - 1 = 0

The above equation is satisfied by

a = 1 and b = -6