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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

7. Circles in the Coordinate Plane

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Exercise 16 Page 579

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

Center: (0,-2 )
Radius: 6
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 for the variable y.

x^2+y^2+4y=32

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Rewrite

Rewrite 0 as 4-4

x^2+y^2+4y+4-4=32

LHS+4=RHS+4

x^2+y^2+4y+4=36

Write as a power

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

SplitIntoFactors

Split into factors

x^2+y^2+2(y)(2)+2^2=6^2

FacNegPerfectSquare

a^2-2ab+b^2=(a-b)^2

x^2+(y+2)^2=6^2

Write as a difference

(x- 0)^2+(y-( - 2))^2= 6^2

The center of the circle is the point ( 0, - 2), and its radius is 6. Finally, we can graph the circle using this information.

Subchapter links

Communicate Your Answer p.575

Monitoring Progress p.576-578

Exercises p.579-580