body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

5. Circles in the Coordinate Plane

Continue to next subchapter

Exercise 37 Page 802

Use the Midpoint Formula to find the center and the Distance Formula to find the radius.

(x-4)^2+(y-3)^2=25

Practice makes perfect

To write the equation of a circle, we need its center and its radius. Let's calculate these two things one at a time.

Center

The center of a circle is the midpoint of the endpoints of a diameter.

Therefore, to find the coordinates of the center (h,k) we will substitute the given points into the Midpoint Formula.

(h,k)=(x_1+x_2/2,y_1+y_2/2)

SubstitutePoints

Substitute ( 0,0) & ( 8, 6)

(h,k)=(0+ 8/2,0+ 6/2)

▼

Simplify right-hand side

Identity Property of Addition

(h,k)=(8/2,6/2)

Calculate quotient

(h,k)=(4,3)

The center of the circle is (4,3).

Radius

The radius of a circle is half its diameter.

To find it, we can find the distance between the center and any known point on the circumference of the circle. For simplicity, we will use (0,0). Let's substitute this point and the center into the Distance Formula.

d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( 0,0) & ( 4, 3)

d=sqrt(( 4- 0)^2+( 3- 0)^2)

▼

Simplify right-hand side

Subtract terms

d=sqrt((4)^2+(3)^2)

Calculate power

d=sqrt(16+9)

Add terms

d=sqrt(25)

Calculate root

d=5

Because the distance is 5, we know that the radius of the circle is 5.

Equation

Let's recall the general equation of a circle with center ( h, k) and radius r. (x- h)^2+(y- k)^2= r^2 We can substitute the values found above into this equation. (x - 4)^2 + (y - 3)^2 = 5^2 ⇕ (x-4)^2+(y-3)^2=25

Subchapter links

Lesson Check p.800

Practice and Problem-Solving Exercises p.801-803

Standardized Test Prep p.803

Mixed Review p.803