Obj. 60 Circles in the Coordinate Plane
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The student is able to write equations for and graph circles in the coordinate plane. The equation of a circle is (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius. Examples are given of identifying the center and radius from given equations and writing equations from given center and radius or a point on the circle. To graph a circle, you plot the center and draw a curve connecting points that are the radius distance from the center.
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Obj. 60 Circles in the Coordinate Plane
- 1. Obj. 60 Circles in the Coordinate Plane The student is able to (I can): • Write equations and graph circles in the coordinate plane • Use the equation and graph of a circle to solve problems.
- 2. The equation of a circle is based on the Distance Formula. (h, k) (x, y) r ( ) ( ) 2 2 2 1 2 1d x x y y= − + − ( ) ( )22 kyhr x= − + − ( ) ( )22 2 x h y k r− + − =
- 3. Examples Identify the center and radius of the circles. 1. center: (7, 2); radius: 2. center: (—5, 1); radius: 3. center: (0, —3); radius: ( ) ( )22 x 7 y 2 16− + − = 16 4= ( ) ( )22 x 5 y 1 36+ + − = 36 6= ( )22 x y 3 20+ + = 20 2 5=
- 4. To graph a circle once you know its center and radius: • Plot its center • Count the radius from the center up, down, left, and right. • Draw a smooth curve connecting the four points. You can also use a compass. Plot the center as before, open up the compass to the length of the radius, and then draw the circle.
- 5. Examples Write the equation of each circle. 1. A with center A(4, —2) and radius 3 2. B with center B(—6, 3) that passes through (—2, 6) ( ) ( )( ) 22 2 x 4 y 2 3− + − − = h k ( ) ( )22 x 4 y 2 9− + + = h k x y ( )( ) ( ) 2 2 2 2 66 3 r− + −−− = 2 25 r= ( ) ( )22 x 6 y 3 25+ + − =