Graphing circles 2

The  exercise appears under the Algebra II Math Mission. This exercise practice graphing circles in a more general form.

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


 * 1) Graph the circle: This problem provides an equation of a circle in a general form and a coordinate plane. The student is asked to graph the circle on the plane, which will likely require changing the form into a convenient graphing form by completing the square.Gracir2.png

Strategies
Knowledge of all the conics and the process of completing the square are encouraged to ensure success on this exercise.
 * 1) Use the technique of completing the square to put the equation in a more convenient form.
 * 2) After factoring,
 * 3) the translations are the opposite of the numbers located with the x and the y.
 * 4) the radius is the square root of the number on the right of the equals sign.
 * 5) After moving the center, select any point on the circumference of the circle to grow it's radius.
 * 6) The default radius is always two.

Real-life Applications

 * 1) Conics have uses in optics, for making mirrors to reflect light, and acoustics, to amplify sounds.
 * 2) Conics model motion of celestial bodies due to laws of physics.