The document discusses equations for circles. It provides the standard form of a circle equation (x-h)2 + (y-k)2 = r2 where (h,k) represents the center and r is the radius. Examples are given of writing the equation of a circle given the center and radius, finding the center and radius from a circle equation, and determining if a line or point lies on a circle. Diagrams illustrate key concepts like tangency.

1. Find the equation of the
circle with radius 3 that is
centered at the origin (x, y)
x2 + y2 = 32 3
y
x
x2 + y2 =9

2. Find the equation of the
circle with radius r that is
centered at the origin (x, y)
x2 + y2 = r2 r
y
x

3. Find the equation of the
circle with radius r that is
centered at (h, k) (x, y)
(x- h)2 + (y-k)2 = r2 r
y-k
(h, k) x-h

4. Write an equation for the circle with center (5,3)
and radius 4
(h, k)
(x- h)2 + (y-k)2 = r2
(x - 5)2 + (y - 3)2 = 42
(x - 5)2 + (y - 3)2 = 16

5. Write an equation for a circle if the endpoints of the
diameter are at (2, 8) and (2, –2).
(x- h)2 + (y-k)2 = r2 (2,8)
(2,3)

6. Write an equation for a circle with center at (3, 5) that
is tangent to the y-axis.
(h, k)
(x - h)2 + (y - k)2 = r2
(x - 3)2 + (y - 5)2 = r2
3

7. Find the center and radius of the circle with equation
Then graph the circle.
(x- h)2 + (y-k)2 = r2
Center: (–3, 0)
Radius: 4

8. Find the center and radius of the circle with equation
Then graph the circle.
x2 + 8x + 16 + y2 – 4y + 4 = -11 + 16 + 4
(x + 4)2 + (y – 2)2 = 9
Center: (–4, 2)
Radius: 3
(x- h)2 + (y-k)2 = r2