1. Equations of Circles (x – a)2 + (y – b)2 = r2
(a, b) = center of the circle
r = radius of the circle
(x – 4)2 + (y + 3)2 = 36
What is the center and the radius of this circle?
(4, -3) = center of the circle
6 = radius of the circle

2. Let’s Look at the Graph of (x – 4)2 + (y + 3)2 = 36
radius
of the circle
is 6
center of
the circle
is (4, -3)

3. Equations of an Ellipse
Standard Form
Intercept Form
The center is the origin
The center is the origin
The center is the origin
The center is the origin

4. Let’s Look at the Graph of 16x2 + 36y2 = 576
center of
the ellipse
is the origin
x-intercepts
are 6
y-intercepts
are 4

5. Rewriting the Equation of an Ellipse
Rewrite the following equation of an ellipse in intercept form.
Rewrite the following equation of an ellipse in standard form.
Just switch the coefficients of x and y.
Since the equation must be equal to 1, divide by 400.
Multiply by the common denominator.
Simplify the fractions.
Simplify the equation.
I think I can do this without having to do too much work.

6. Graphing Circles and Ellipses
Graph the following circle.
Write the equation of the circle whose graph looks like this. 8 6 4 2 -2 -4 -6 -8 8 6 4 2 -2 -4 -6 -8 8 6 4 2 -2 -4 -6 -8
Graph the following ellipse.
Write the equations of the following two ellipses in both standard form and intercept form.

7. Equations of a Hyperbola
xy = k
As x increases, y decreases so that the product of x and y is always k
xy = 8
As x increases, y decreases so that the product of x and y is always 8
A hyperbola is a function
The coordinate axes are asymptotes of the graph
When k > 0, the graph is in quadrant I and quadrant III
When k < 0, the graph is in quadrant II and quadrant IV
Each branch of the hyperbola is the reflection of the
other in the origin

8. Let’s Look at the Graph of xy = 8
Since k > 0, the graph is in quadrant I and quadrant III
The x and y axes are asymptotes of the graph

9. Let’s Look at the Graph of xy = -8
Since k < 0, the graph is in quadrant II and quadrant IV
The x and y axes are asymptotes of the graph

10. Graphing Hyperbolas Solve the equation for y. Make a table of values.x y x y
Since k is positive, the graph is in quadrants I and III
Since k is negative, the graph is in quadrants II and IV

11. More Graphing Hyperbolas
Solve the equation for y.
Make a table of values. x y x y
Since k is positive, the graph is in quadrants I and III
Since k is positive, the graph is in quadrants I and III