11.5: Circles in the Coordinate Plane OBJECTIVES: STUDENTS WILL BE TO… IDENTIFY THE CENTER AND THE RADIUS OF A CIRCLE FROM ITS EQUATION WRITE AND GRAPH THE EQUATION OF A CIRCLE

Circle  A set of all points in a plane that are a given distance, the radius, from a given point, the center

Standard Equation of a Circle  Standard equation of a circle with center ( h, k ) and radius r (x – h ) 2 + (y – k ) 2 = r 2

Write the equation of the circle with center (-1,3) and a radius of 2. h = -1 k= 3 r = 2 Plug values into standard equation: (x – (-1)) 2 +(y – 3) 2 = (2) 2 (x + 1) 2 + (y-3) 2 = 4 notice #’s are opposite sign of what is given

Write the equation of the circle with the given center and radius. a.) center (3,5); radius = 6 b.) center (-2,-1); radius = c.) center (0, 0); radius = 5

If r 2 = (x-h) 2 + (y – k) 2, then…. You can use this to find the radius of a circle and write the equation.

Write the standard form of the circle with center (2,3) that passes through the point (-1,1). h = 2 k= 3 x= -1 y= 1 Write the equation using h, k, and r:

Write the standard form of the circle with the given center that passes through the given point. 1.) center (-2,6); point (-2, 10) 2.) center (7, -2); point (1, -6)

Graphing a circle:  Find the center and radius of the circle  Plot the center  Draw radius. Use compass to draw circle with the given radius.

Find the center and radius of the circle with the given equation. Then graph the circle. (x + 7) 2 + (y -5) 2 = 16 h= -7 k= 5 r= 4 Center (-7, 5), radius = 4

Find the center and radius of the circle with the given equation. Then graph the circle. x 2 + y 2 = 9

Find the center and radius of the circle with the given equation. Then graph the circle. (x – 2) 2 + (y – 3) 2 = 100

Application A diagram locates a radio tower at (6, -12) on a coordinate grid where each unit represents 1 mile. The radio signal’s range is 80 miles. Find an equation that describes the position and range of the tower.

Write the equation of the circles graphed below: