Warm Up Conics
1. Write the general equation for a circle.
2. How do you graph a circle?
3. Write the general equation for an ellipse that is vertical and centered at
(1,2).
4. What equation do you use for ellipses that relates vertex, covertex, and
foci?
Standard form for the equation of an ellipse centered at (h,k):
Major Axis
Equation
Horizontal
( x h) 2 ( y k ) 2
a2
b2
Vertical
( y k ) 2 ( x h) 2
a2
b2
1
1
Vertices
(h+a,k) and (h-a,k)
(h, k+a) and (h, k-a)
(h+c,k) and (h-c,k)
(h, k+c) and (h, k-c)
(h,k
4.3-4.4 Circles
Intermediate Algebra
Circle
(x,y)
The distance formula can be used to find a
general equation for a circle with center (h,k)
and radius r:
Ex 1: Write the equation of the circle with center (-3,4) and radius 6.
Ex 2: Write the equation of
Ex 3: Write the equation of the circle with center (2,4) and containing the point
(8,12).
4.3-4.4 Ellipses
Algebra 2H
Ellipse
focus of an ellipse
major axis
vertices of an ellipse
minor axis
co-vertices of an ellipse
Formal definition of an ellipse: the s
Circle and Ellipse Activity Partner 1
Graph the following conic sections.
If it is an ellipse find the center, vertices, and co-vertices.
If it is a circle find the center and radius.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Circle and Ellipse Activity Partner 2
Write the equation of the following conic sections.
If it is an ellipse or hyperbola identify the center, vertices, and co-vertices.
If it is a circle identify the center and radius.
Graph the following conic sections
Conic Sections
Intermediate Algebra Chapter 4
While some conic sections are functions, not all of them are. Sometimes it is
necessary to use two functions to graph a conic section.
1
4.3-4.4 Circles
Intermediate Algebra
Circle
(x,y)
The distance formula c
Helpful Reminders/Ways to Solve Exponential and Logarithmic Equations
1. 4x =642x +1
2. lnx = -1
3. 10x = 300
4. 2(5x ) = 32
5. 6x = 45
One-to-One Property (get the same base)
Rewrite in exponential form and solve
Apply the log or ln to both sides
Isolate
Circle, Ellipse, and Hyperbola Activity Partner 1
Graph the following conic sections.
If it is an ellipse or hyperbola, find the center, vertices, and co-vertices.
If it is a circle find the center and radius.
1.
2.
3.
4.
5.
Write the equation of the foll