Big Ideas Math Geometry, 2014
BI
Big Ideas Math Geometry, 2014 View details
Chapter Review
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Exercise 47 Page 586

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

Center: (6,- 4)
Radius: 2

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+y^2-12x+8y+48=0
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Rewrite
x^2+y^2-12x+8y+36+16-4=0
x^2-12x+36+y^2+8y+16-4=0
x^2-12x+36+y^2+8y+16=4
x^2-12x+6^2+y^2+8y+4^2=2^2
x^2-2(x)(6)+6^2+y^2+2(y)(4)+4^2=2^2
(x-6)^2+y^2+2(y)(4)+4^2=2^2
(x-6)^2+(y+4)^2=2^2

a+b=a-(- b)

(x- 6)^2+(y-( - 4))^2= 2^2
The center of the circle is the point ( 6, - 4), and its radius is 2. Finally, we can graph the circle using this information.