Feel free to move the red and green points and/or the circle anywhere you'd like. Notice something?[br]See a right angled triangle? Does it ring a bell? Assume the distance between the red point and [math]\left(h,k\right)[/math] as [math]r[/math].Can you think of a relation between [math]\left(x,y\right)[/math] and [math]\left(h,k\right)[/math]? [br]
[b]Standard Form of the Equation of a Circle in the Coordinate Plane[br]For a given [math]\left(h,k\right)[/math] and a given red point the distance between [math]\left(h,k\right)[/math] and [math]\left(x,y\right)[/math] remains same wherever [math]\left(x,y\right)[/math] may be.[br][/b][br]By the Pythagorean Theorem, [br][br][math]\left|x-h\right|^2+\left|y-k\right|^2=r^2[/math]. Since the absolute value of any quantity is never negative, we can write[br][br][math]\left(x-h\right)^2+\left(y-k\right)^2=r^2[/math]. [br][br]