Question

The point (1, 2) lies inside the circle x² + y² – 2x + 6y + 1 = 0.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Given equation of circle is x² + y² – 2x + 6y + 1 = 0

Here 2g = – 2 ⇒ g = – 1

2f = 6 ⇒ f = 3

∴ Centre = (– g, – f) = (1, – 3)

And r = `sqrt(g^2 + f^2 - c)`

= `sqrt(1 + 9 - 1)` = 3

∴ Distance between the point (1, 2) and the centre (1, – 3)

= `sqrt((1 - 1)^2  (2 + 3)^2)` = 5

Here 5 > 3, so the point lies outside the circle.