Page 174 - Math Course 3 (Book 2)

Circles: Equations

Your Turn!
y
y = –1
Equation of a Circle
Write an equation for a circle with center at (0, –5),
5 units (4, 2) d = 18.

A. x² + (y – 5)² = 81
O 5 units B. x² + (y + 5)² = 324
x C. x² + (y – 5)² = 324
y = –3 D. x² + (y + 5)² = 81
Answer

An equation for the circle is
Answer
(x – 4)² + (y – 2)² = 25.

Graph a Circle

Example

Graph (x – 2)² + (y + 3) ² = 4.
Use Characteristics of Circles
Compare each expression in the equation to the A circle with a diameter of 8 has its center in the
standard form. second quadrant. The lines y = –1 and x = 1 are
tangent to the circle. Write an equation of the
(x – h)² = (x – 2)² (y – k) ² = (y + 3) ² circle.
x – h = x – 2 y – k = y + 3 A. (x – 1)² + (y + 1)² = 16
–h = –2 –k = 3 B. (x – 3)² + (y + 3)² = 16
C. (x + 3)² + (y – 3)² = 16
h = 2 k = –3 D. (x + 3)² + (y + 3)² = 64
r² = 4, so r = 2.

The center is at (2, –3), and the radius is 2. Answer

Graph the center. Use a compass set at a width of
2 grid squares to draw the circle.

Answer
y

O X

(2, –3)

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