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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

8. Equations of Circles

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Exercise 8 Page 778

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

Center: (0,- 1)
Radius: 2
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.

x^2+(y+1)^2=4

▼

Rewrite

Write as a power

x^2+(y+1)^2=2^2

a+b=a-(- b)

x^2+(y-(- 1))^2=2^2

Rewrite x^2 as (x-0)^2

(x- 0)^2+(y-( - 1))^2= 2^2

The center of the circle is the point ( 0, - 1), and its radius is 2. Finally, we can graph the circle using this information.

Subchapter links

Exercises p.778-781