geometry honors section 9.6 circles in the coordinate plane
TRANSCRIPT
Geometry Honors Section 9.6
Circles in the Coordinate Plane
If you graph the equation y = 3x + 5, its graph is a ____ so it is called a ______ equation.
linelinear
For the equation y = 3x + 5, 3 is the ______ of the line and 5 is the __________ of the line.
Just by looking at the equation, you can determine the slope and y-intercept of the line without graphing. For this reason, the equation is said to be written in _____________ form.
slopey-intercept
slope-intercept
Similarly, there is a special form for the graph of a circle. This equation
has the unofficial name of the form of a circle.center- radius
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 =
HO =
KO =
2 21 2 1 3 5
2 26 2 6 3 5
2 21 2 7 3 5
In addition to equaling the same distance, what do the three
distance formula have in common?
2 2__ 2 __ 3
Using x and y as coordinates of any point on the circle, what would the distance formula look like for OO?
2 2x h y k r
Squaring both sides we get the center-radius form of a circle.
Center:_______Radius: _______
2 2 2x h y k r
(h , k)r
Example 1: Write an equation for the circle with the given center and radius.
a) center: (4, 3) radius = 7
b) center (5, -2) radius =
2 24 3 49x y
2 25 2 27x y
3 3
Example 2: Find the center and radius of each circle.
a) center ( ____ , ____ ) r = _____
b) center ( ____ , ____ ) r = _____
2 2( 4) ( 3) 43x y
2 25 100x y
3 4 43
0 5 10
Example 3: Write the equation of the circle to the right.
2 2( 2) 16x y
Example 4: Write an equation of a circle with a center of (3, 4) containing the point (8, -8).
2 23 8 4 8 13
22( 3) 4 169x y