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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

5. Circles in the Coordinate Plane

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Exercise 45 Page 802

How can you find the radius of a circle if you know its area?

(x-4)^2+(y-7)^2=36

Practice makes perfect

To begin, let's recall the formula for the area of a circle. A=π r^2 We will find the radius of our circle by substituting 36π for A in this equation.

A=π r^2

A= 36π

36π=π r^2

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Solve for r

.LHS /π.=.RHS /π.

36=r^2

sqrt(LHS)=sqrt(RHS)

6=r

Rearrange equation

r=6

Note that the radius of a circle is a measure of distance. This is why we did not consider the negative value of the square root. Let's now recall the standard form of an equation of a circle. (x-h)^2+(y- k)^2= r^2 In this formula, (h, k) is the center of the circle and r is its radius. We are told that the center of the circle is (4, 7). This information, together with r= 6, is enough to write the equation. (x-4)^2+(y- 7)^2= 6^2 ⇕ (x-4)^2+(y-7)^2=36

Subchapter links

Lesson Check p.800

Practice and Problem-Solving Exercises p.801-803

Standardized Test Prep p.803

Mixed Review p.803