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
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