Question

If the acute angle between the lines 3x² – 4hxy + 3y² = 0 is 30°, then h = ______.

Options

• `+- 1/sqrt(3)`

• `+- sqrt(3)/2`

• `+- sqrt(3)`

• `+- 5/2`

Answer 1

If the acute angle between the lines 3x² – 4hxy + 3y² = 0 is 30°, then h = `+- sqrt(3)`.

Explanation:

Given equation is 3x² – 4hxy + 3y² = 0

∴ A= 3, B = 3, H = –2h

`tan theta = |(2sqrt("H"^2 - "AB"))/("A" + "B")|`

⇒ `1/sqrt(3) = |(2sqrt(4"h"^2 - 9))/6|` 

⇒ h = `+- sqrt(3)`