Equation of a circle in non-factored form

The  exercise appears under the Geometry Math Mission. This exercise uses the equation of a circle to determine the center and radius of the circle.

Types of Problems
There is one type of problem in this exercise:


 * 1) Determine the information from the equation: This problem provides the equation of a circle. The student is asked to use the equation to determine the center and radius of the circle that is presented.Eoacinff1.png

Strategies
Knowledge of the circle equation, functional transformations, and the algebraic technique of completing the square are encouraged to ensure success on this exercise.
 * 1) When the equation of a circle is written in the factored form of $$ (x-h)^2+(y-k)^2=r^2$$ the center will be at $$(h,k)$$ and the center will be $$r$$.
 * 2) To write a non-factored equation in factored form, the technique of completing the square is useful.
 * 3) To complete the square for $$x^2+bx$$, add (and subtract) the quantity $$ (\frac{b}{2a})^2$$.
 * 4) The center of the circle can be understand as a horizontal and vertical translation which can assist with accuracy and efficiency.

Real-life Applications

 * 1) The circle is one of the conics which have applications in acoustics and optics.
 * 2) The unit circle can be used as a memorization device for basic trigonometric values.
 * 3) Circles can be used to model certain periodic behaviors and various forces in physics, such as centripedal and centrifugal motion.