Name: _____________________
Circles Notes
Circle: set of points in a plane that are a fixed distance, called the radius, from a fixed point, called the
center.
(x, y)
r
Equation for a circle: The circle with center ( h, k ) and radius r has the equation
C (h, k)
Derive using Pythagorean theorem:
Formula in Standard Form:
Examples:
1. Draw the circle
a. y 2  4  x 2
b. ( x  2)2  ( y  6) 2  4
c. ( x  1)2  9  y 2
1
-1
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
2. The point (-2, 5) is on a circle centered at the
origin. Write the equation of the circle.
3. Find an equation of the circle with center (3, -4)
and radius 3
4. Write each equation of the circle in standard form. State its center and radius.
2
2
2
2
a. x  y  10 x  4 y  21  0
b. 2 x  2 y  12 x  4 y  2  0
A little harder c:
1 2 1 2
x  y  y  2x  7  0
2
2
Circle WKST
Graph the equations.
1. ( x  4)2  ( y  5)2  4
2. ( x  3)2  y 2  36
If the graph of the given equation is a circle, find its center and radius. If the equation has no graph, say so.
3. x2  y 2  8x  2 y  18  0
4. x 2  y 2  3x  4 y  0
If the graph of the given equation is a circle, find its center and radius. If the equation has no graph, say so.
5. 4 x2  4 y 2  16 x  24 y  36  0
6. 16 x2  16 y 2  32 x  8 y  0
Find an equation of the circle described. (A sketch may be helpful.)
7. Center (-2, 0); passes through (2, 0)
8. Find an equation of the circle described. (A sketch may be helpful.)
A diameter has endpoints (2, 5) and (0, 3).
9. Find an equation of the circle described. (A sketch may be helpful.)
Center on line y  4  0 ; tangent to x-axis at (-2, 0)
10. Find an equation of the circle described. (A sketch may be helpful.)
Center in quadrant four; tangent to the lines x  1, x  9, and y  0.
11. The signals of a television station can be received up to 98 miles away. Your house is 50 miles east and 67
miles south of the station. Can you receive the station’s signals?
12. The circle defined by ( x  1)  ( y  4)  16 is translated 3 units to the left and 2 units down. Write the
standard equation for the resulting circle.
2
2