Geometry Honors Section 9.6
Circles in the Coordinate Plane
If you graph the equation
line so it
y = 3x + 5, its graph is a ____
linear equation.
is called a ______
For the equation y = 3x + 5, 3 is the
slope of the line and 5 is the
______
y-intercept of the line.
__________
Just by looking at the equation, you
can determine the slope and yintercept of the line without graphing.
For this reason, the equation is said to
slope-intercept form.
be written in _____________
Similarly, there is a special form for
the graph of a circle. This equation
has the unofficial name of the
center- radius form of a circle.
Recall that a circle is the set of points
in a plane, that are equidistant
from a given point.
Example 1: Use the distance formula to
determine the three distances below. Show your
initial use of the distance formula.
CO =
 1  2  1  3
2
2
5
HO =  6  2   6  3  5
2
2
KO =  1  22   7  32  5
In addition to equaling the same
distance, what do the three
distance formula have in common?
 __  2   __  3
2
2
Using x and y as coordinates of any
point on the circle, what would the
distance formula look like for OO?
 x  h   y  k   r
2
2
Squaring both sides we get the
center-radius form of a circle.
 x  h   y  k 
2
2
r
(h , k)
Center:_______
r
Radius: _______
2
Example 1: Write an equation for the
circle with the given center and radius.
a) center: (4, 3)
radius = 7
 x  4    y  3
2
2
 49
b) center (5, -2) radius = 3 3
 x  5   y  2 
2
2
 27
Example 2: Find the center and radius
of each circle.
( x  4)  ( y  3)  43
2
2
43
a) center ( ____
 4 , ____
3 ) r = _____
 x  5
2
 y  100
2
b) center ( ____
10
5 , ____
0 ) r = _____
Example 3: Write the equation of the circle to the right.
x  ( y  2)  16
2
2
Example 4: Write an equation of a circle with a
center of (3, 4) containing the point (8, -8).
 3  8   4  8  13
2
2
( x  3)   y  4   169
2
2
Example: The equation of a circle is x2 + y2 – 6x + 2y = b.
Find the center of the circle.
I need the equation in the form (x - h) 2  ( y  k ) 2  r 2 .
How do I do this?
Complete the square!!!!
x 2  6 x  ___  y 2  2 y  ___  b
x2  6x  9  y2  2 y 1  b  9 1
(3,1)
x  32   y  12  b  10
If the radius of the circle is 8 units, determine the value of b.
b  10  64
b  54
Fix problems 13 & 14 in the HW
13. x2 + 8x + y2 +12y = 13
14. x2 - 10x + y2 +3y = 10