Question

The line x + 3y = 0 is a diameter of the circle x² + y² + 6x + 2y = 0.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Given equation of the circle is x² + y² + 6x + 2y = 0

Centre is (– 3, – 1)

If x + 3y = 0 is the equation of diameter

Then the centre (– 3, – 1) will lie on x + 3y = 0

– 3 + 3(– 1) = 0

⇒ – 6 ≠ 0

So, x + 3y = 0 is not the diameter of the circle.