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McGraw Hill Integrated II, 2012 View details

8. Equations of Circles

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Exercise 7 Page 778

Adapt the given equation to match the standard equation of a circle.

Center: (3,- 2)
Redius: 4
Graph:

Practice makes perfect

Let's start by recalling the standard equation of a circle. (x- h)^2+(y- k)^2= r^2Here, the center is the point ( h, k) and the radius is r. We will rewrite the given equation to match this form, and then we can identify the center and the radius. In this case, we will need to complete the square twice — once for each variable.

x^2-6x+y^2+4y=3

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Rewrite

AddEqn

LHS+9+4=RHS+9+4

x^2-6x+y^2+4y+9+4=3+9+4

CommutativePropAdd

Commutative Property of Addition

x^2-6x+9+y^2+4y+4=3+9+4

AddTerms

Add terms

x^2-6x+9+y^2+4y+4=16