Circles. How to Graph Them From The Equation. Finding The Equation From The Graph.

What are the steps to graph a circle from its equation? What if the equation is not in standard form? ... OK, I have to complete the square to factor binomials for x and y; but how this can be done without altering the equation?

Most textbooks will assume that you know how to complete the square and will skip intermediate steps. This lesson won't let you in the limbo. You will see each one of the involved steps! Scroll down the page to find some additional help with formal definitions of important concepts related to the lesson. Also at the upper part of the screen you may find the MARKER TOOLS menu that may be used to complete the companion problem given after one of the examples.

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

Center: In a circle, it is the point from which all the points in the circle are equidistant.

Circle: It is made of the set of all points in a plane laying at a constant distant r from a given point called center. If the radius is r and the center at (h,k) then the equation of the circle is given by  (x-h)2 + (y-k)2 = r2

Completing the Square: Method that finds the constant term in an incomplete perfect square trinomial of a second degree equation to solve it.

Conic section: A figure that is obtained slicing a double cone with a plane. (parabola, circle, hyperbola, and ellipse)

Factoring: The process to brake a polynomial down into the product of several factors.

Factors: All whole numbers that are multiplied together to yield another number.

Factored Form: Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial.

Radius: For a circle the radius is the segment with endpoints at the center of the circle and the circle.

Standard form of an equation of a circle: 

(x-h)2 + (y-k)2 = r2 where (h,k) is the center and r is the radius.


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