# Application of Completing the Square

Completing the square is used to find the radius and center of circles. The standard form for a circle is $$ax^2+by^2+cx+dy+e =0$$. To find the radius and center of the circle the equation will need to be in the form $$(x-h)^2+(y-k)^2 = r^2$$ where center is ($$h,k$$) and the radius is $$r$$.

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Features of a circle from its expanded equation | Khan Academy

Completing the square is also used to find the center and vertices of an ellipse.