CK12 - Geometry

In orderto writethe equationof the circlein this example,we needto find the centerof the circleand the
radiusof the circle.

Let’s graphthe two pointson the coordinateplane.

We see that the centerof the circlemustbe in the middleof the diameter.

In otherwords,the centerpointis midwaybetweenthe two points and. To get frompoint to

point , we musttravel unitsto the right and unitsup. To get halfwayfrom point to point , we

must travel units to the rightand units up. Thismeans the center of the circle is at point

or.

We find the lengthof the radiususingthe PythagoreanTheorem:

Thus,the equationof the circleis:

Completingthe Square:

You saw that the equationof a circlewith centerat point ) and radius is givenby:

This is calledthestandardformof the circleequation.The standardform is very usefulbecauseit tells us
right awaywhatthe centerand the radiusof the circleis.

If the equationof the circleis not in standardform,we use the methodofcompletingthe squareto rewrite
the equationin the standardform.

Example 8

Find the centerand radiusof the followingcircleand sketcha graphof the circle.

To find the centerand radiusof the circlewe needto rewritethe equationin standardform.The standard

equationhas two perfectsquarefactorsone for the termsand one for the terms.We needto complete

the squarefor the termsand the termsseparately.