8/18/2019 Equation of a Circle...Find the center & radius..complete the square.docx

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Name ________________ Date _______  

Find the center and the radius by completing the square.

 

Directions: Find the center and radius of the circle given the following equation: 

4 x 2 + 4 y

2 – 16 x  – 24 y + 51 = 0.

Here is the equation they've given you.

Move the loose number over to the other

side.

Group the x-stuff together. Group the y-stufftogether.

Whatever is multiplied on the squared terms(it'll always be the same number) divide it offfrom every term.

!his is the "ompli"ated step. #ou'll needspa"e inside your groupings be"ause this is

where you'll add the squaring term. !a$e

the x-term "oeffi"ient multiply it by one-halfsquare it and then add this to both sides ofthe equation as shown. %o the same with

the y-term "oeffi"ient. &onvert the left side tosquared form and simplify the right side.

ead off the answer from the rearranged

equation.

!he "enter is at (h, k ) = ( x, y) = (2, 3).!he radius is

r  =   √ 1/4

= 1/2