Question

Determine whether the points P(1, 0), Q(2, 1) and R(2, 3) lie outside the circle, on the circle or inside the circle x² + y² – 4x – 6y + 9 = 0.

Answer 1

The equation of the circle is x² + y² – 4x – 6y + 9 = 0

`"PT"^2 = x_1^2 + y_1^2 - 4x_1 - 6y_1 + 9`

At P(1, 0), PT² = 1 + 0 – 4 – 0 + 9 = 6 > 0

At Q(2, 1), PT² = 4 + 1 – 8 – 6 + 9 = 0

At R(2, 3), PT² = 4 + 9 – 8 – 18 + 9 = -4 < 0

The point P lies outside the circle.

The point Q lies on the circle.

The point R lies inside the circle.