Find an equation of the circle with centre C(5, -3) that passes through the point A(-2, 1) in the form (x-a)^2 + (y-b)^2 = k

step 1 remember than the a and b terms locate the centre of the circle on the axis so we can substitute in the centre values for a and b. (x-5)^2 + (y-(-3))^2 = k. (x-5)^2 + (y+3)^2 = k.

Step 2. k is a constnat representing the radius squared. calculate the radius of the circle using pythaogras. distance from centre to point A in the x direction is 5-(-2)=7. distance from centre to point B in the y direction is 1-(-3)= 4. using pythagoras we know that A^2=B^2 + C^2. this means the radius^2 = X distance^2 + Y distance^2.
so r^2 = 7^2 + 4^2. r^2 = 49+16=65.

Step 3. putting both centre component and radius together we obtain (x-5)^2 + (y+3)^2 = 65. This is the equation of the circle.