A circle C with centre at the point (2, –1) passes through the point A at (4, –5). Find an equation for the circle C.

You would start with this equation (x – a)² + (y – b)² = r², with the center being at the point (a, b) and the radius being "r". Therefore you would have (x-2)²+(y+1)²=r², in order to determine the radius we must the pythagoras theorem. So we make a right angle triangle with points and A and C where the hypotenuse will be the radius. So we would do (4-2)²+(-5--1)² which is equal to 20 so the r is equal to the square root of 20. Finally to complete the question, the equation to the circle would be (x-2)²+(y+1)²=20