Circles And Circular Functions Worksheet - Dr. Neal, Math 116 - 2008
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5Dr. Neal, Fall 2008
MATH 116
Circles and Circular Functions
A circle is defined to be the collection of all points ( x , y ) that are equidistant from a
fixed center point (h , k ). The distance to this center point is called the radius r .
A Circle Centered at the Origin
Suppose a circle is centered at the origin (0, 0) and has a radius of length r . Then a
point ( x , y ) on the circle creates a right triangle with sides having lengths x and y , and
the hypotenuse having length r . By the Pythagorean Theorem, we can say
2
2
2
+ y
= r
x
(x, y)
r
y
x
2
2
2
+ y
= r
So x
is the equation of a circle centered at the origin with radius r .
Example 1. Give the equation of the circle centered at (0, 0) with radius 9/5. What
points are on the circle for x = –6/5?
81
2
2
2
+ y
=
Solution. Using r = 9/5, then r
= 81/25; so the equation becomes x
.
25
2
6
81
36
81
2
2
−
+ y
=
→
+ y
=
→
For x = –6/5, there are two possible y -values:
5
25
25
25
9 × 5
81
36
45
45
3 5
2
2
=
−
→ y
=
→ y = ±
= ±
= ±
. So the two points on the
y
25
25
25
25
5
5
6
3 5
circle are −
, ±
5
5
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