Question

Determine whether the points (– 2, 1), (0, 0) and (– 4, – 3) lie outside, on or inside the circle x² + y² – 5x + 2y – 5 = 0

Answer 1

To find the position of a point with regard to a given circle

Substitute the point in the equation of the circle

If we get a positive value, the point lies outside the circle.

If we get a – ve value the point lies inside the circle and

if we get O then the point lies on the circumference of the circle.

The given circle is x² + y² – 5x + 2y – 5 = 0  .......(1)

Substituting the point (– 2, 1) in (1) we get

4 + 1 – 5(– 2) + 2(1) – 5 = 5 + 10 + 2 – 5 = 12

⇒ (– 2, 1) lies outside the circle

Substituting the point (0, 0) in (1) we get

– 5 < 0

⇒ (0, 0) lies inside the circle Substituting the point (– 4, – 3) in (1)

We get 16 + 9 + 20 – 6 – 5 = 34 >0

⇒ (– 4, – 3) lies outside the circle