10-1: The Circle Objectives: Use the standard and general forms of the equation of a circle Graph circles ©2002 Roy L. Gover (www.mrgover.com)

Applications The Chunnel Gears The Circle: Wheels

Definition P(x,y) The circle is the locus (set) of all points that are equidistant from a given point called the center. Radius Center (h,k)

Definition The standard form of the equation of a circle with radius r and center at (h,k) is:

Example Write the equation of the circle with center at (4,-1) and radius of 6 units. Then graph the equation. Hint: h=4, k=-1 & r2=36

Try This Write the equation of the circle with center at (-5,6) and radius of 5, then graph the equation.

Solution h=-5 k=6 (-5,6)

Example Graph the circle with center at (4,-5) and radius 4 using a graphing calculator ...

Steps: 1. Write equation in standard form. 2. Solve for y 3. Enter in calculator: y1 & y2 4. Set window- use Z-Square to make round

Try This Graph the circle with center at (-2,-1) and radius 2 using a graphing calculator ...

Solution h=-2 & k=-1, therefore: ...

Solution

Example The equation of a circle is: Find the radius and coordinates of the center. Hint: Change to standard form by completing the square

Try This The equation of a circle is: Write the equation in standard form. Find the radius and coordinates of the center.

Try This The equation of a circle is: Find the radius and coordinates of the center. Radius=4; Center: (1,-3)

Lesson Close 1. What is h & k ? 2. What is the center & radius of: