College Algebra 1.9 Circles

Objectives Write the standard form of the equation of a circle. Graph a circle by hand and by using the calculator. Work with the general form of the equation of a circle.

Standard Form A circle is the set of all points equidistant from a fixed point called the center. The distance is the radius. (x-h) 2 + (y-k) 2 = r 2 (h, k) is the center, r is the radius

If the center is at (0,0) then the equation is x 2 + y 2 = r 2 If r= 1, then it is the unit circle, and has the equation x 2 + y 2 = 1

Example 1 Write the standard form of each circle. A. Radius 5 Center (3, 2) B. Radius 15 Center (-4, 8)

Graphing a Circle By Hand Example 2: Graph the equation (x-4) 2 + (y+2) 2 = 25

Graphing a Circle on the Calculator You must get y by itself, then type both equations into the calculator. (x-4) 2 + (y+2) 2 = 25

Example 3 Find the intercepts of the circle (let y=0) (x+5) 2 + (y-2) 2 = 36

General Form x 2 + y 2 +ax +by + c = 0 If given general form, to graph, rewrite in standard form.

Example 4 Graph the circle. x 2 + y 2 - 6x +2y + 9 = 0

Assignment Page 185: 1-8 all, 9-45 odds