A circle has centre (2, -3) and a radius of 5 units. Which of these points lies on the circle?

1. A point lies on a circle when its distance from the centre equals the radius. 2. It is easier to compare squared distances, so test whether the squared distance equals 25. 3. For the point 6 comma 0 the horizontal gap is 6 minus 2, which is 4, and 4 squared is 16. 4. The vertical gap is 0 minus minus 3, which is 3, and 3 squared is 9. 5. Sixteen plus 9 is 25, which matches the radius squared, so this point lies on the circle. 6. For 2 comma 3 the gaps are 0 and 6, giving 0 plus 36, which is 36 and too large. 7. For 0 comma 0 the gaps are 2 and 3, giving 4 plus 9, which is 13 and too small, and for 4 comma 2 the gaps are 2 and 5, giving 4 plus 25, which is 29. 8. The point 2 comma 3 is the trap for changing the sign of the y coordinate of the centre instead of subtracting it. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 7: Analytical geometry_