Splash Screen. Then/Now You wrote equations of lines using information about their graphs. Write the equation of a circle. Graph a circle on the coordinate.

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Presentation transcript:

Splash Screen

Then/Now You wrote equations of lines using information about their graphs. Write the equation of a circle. Graph a circle on the coordinate plane.

Concept

Example 1 Write an Equation Using the Center and Radius A. Write the equation of the circle with a center at (3, –3) and a radius of 6. (x – h) 2 + (y – k) 2 = r 2 Equation of circle (x – 3) 2 + (y – (–3)) 2 =6 2 Substitution (x – 3) 2 + (y + 3) 2 = 36Simplify. Answer:

Example 1 Write an Equation Using the Center and Radius B. Write the equation of the circle graphed to the right. (x – h) 2 + (y – k) 2 = r 2 Equation of circle (x – 1) 2 + (y – 3) 2 =2 2 Substitution (x – 1) 2 + (y – 3) 2 = 4Simplify. Answer: The center is at (1, 3) and the radius is 2.

Example 1 A.(x – 2) 2 + (y + 4) 2 = 4 B.(x + 2) 2 + (y – 4) 2 = 4 C.(x – 2) 2 + (y + 4) 2 = 16 D.(x + 2) 2 + (y – 4) 2 = 16 A. Write the equation of the circle with a center at (2, –4) and a radius of 4.

Example 1 A.x 2 + (y + 3) 2 = 3 B.x 2 + (y – 3) 2 = 3 C.x 2 + (y + 3) 2 = 9 D.x 2 + (y – 3) 2 = 9 B. Write the equation of the circle graphed to the right.

Example 3 Graph a Circle The equation of a circle is x 2 – 4x + y 2 + 6y = –9. State the coordinates of the center and the measure of the radius. Then graph the equation. Write the equation in standard form by completing the square. x 2 – 4x + y 2 + 6y= –9Original equation x 2 – 4x y 2 + 6y + 9 = – Complete the squares. (x – 2) 2 + (y + 3) 2 = 4Factor and simplify. (x – 2) 2 + [y – (–3)] 2 = 2 2 Write +3 as – (–3) and 4 as 2 2.

Example 3 Graph a Circle With the equation now in standard form, you can identify h, k, and r. (x – 2) 2 + [y – (–3)] 2 = 2 2 (x – h) 2 + [y – k] 2 = r 2 Answer:So, h = 2, y = –3, and r = 2. The center is at (2, –3), and the radius is 2.

Homework: Pg. 760 #’s 1, 2, 7 and 8