Question

The measure of the angle between lines (sin²θ - 1)x² - 2xy cos²θ + cos²θy² = 0 is ______ 

Options

• `pi/2`

• `pi/6`

• `pi/4`

• `pi/3`

Answer 1

The measure of the angle between lines (sin²θ - 1)x² - 2xy cos²θ + cos²θy² = 0 is `underline(pi/2)`.

Explanation:

Comparing the given equation ax² + 2hxy + by² = 0, we get

a = sin²θ - 1 = -cos²θ, b = cos²θ

Here, a + b = -cos²θ + cos²θ = 0

∴ the lines are perpendicular.

∴ θ = `pi/2`