Circle Notes
Name___________________________
Circle- the set of all points (x,y) in a plane that are equidistance from a fixed point called
the center of the circle.
Radius- distance from center to any point on the circle.
Standard Equation of a Circle with Center at the origin
x2 + y2 = r2 ; where r is the radius
Graphing Circles:
Graph y2 = -x2 + 36
Step 1: Rewrite x2 + y2 = 36
Step 2: Find the radius= 6
Step 3: Plot 6 units from origin in all directions on the x and y axis. Draw circle.
Writing Equation of a Circle
The point (2, -5) lies on a circle whose center is the origin. Write the equation of the
circle.
Step 1: Find the radius by using the distance formula and the center (0,0) and
point (2, -5)
Radius =
(2  0) 2  (5  0) 2  29
Step 2: Write the equation of the circle x2 + y2 = 29
Writing the Equation of a line tangent to a circle.
Write the equation of the line tangent to the circle x2 + y2 = 13 at (-3,2).
Solution: A line tangent to a circle is perpendicular to the radius at the point of tangency.
Because the radius to the point (-3,2) has a slope of -2/3, the slope of the tangent line at
(-3,2) is the negative reciprocal of -2/3 or 3/2. An equation of the tangent line is as
follows:
3
y  2  ( x  (3))
2
3
9
y2 x
2
2
3
13
y  x
2
2
Circles and Inequalities- The regions inside and outside the circle x2 + y2 = r2 can be
described by inequalities, with x2 + y2 < r2 represents the region inside the circle and
x2 + y2 > r2 represents the region outside the circle.
Problem: A cellular phone tower services a 10 mile radius. You get a flat tire 4 miles
east and 9 miles south of the tower. Are you in the tower’s range?
Suppose you fix the tire and then drive south. . For how many more miles will you be in
the range of the tire?