Chapter Sections 9.2-9.3

Question 0

For the equation x^2=4ay , on what axis does the parabola open up and to what direction?
What about x^2=-4ay?

Answer 0

For both equations they open on the y axis so they are reflective over the y axis
The first equation has the parabola open up
The second equation has the parabola open down

Question 1

For the equation y^2=4ax , on what axis does the parabola open up and to what direction?
What about y^2=-4ax?

Answer 1

For both they open on the x axis so the graph is reflective over the x axis

The first equation opens to the right
The second equation opens to the left

Question 2

For the equation x^2= -12y 
What is it? 
Where is the vertex? 
Which way does it go?
What is the a value?

Answer 2

-parabola
-(0,0)
- y axis of symmetry and it opens down
- to find “a”value you equal -4a=-12 to get 3 as “a”
(It is -4a because the parabola opens down…if it opened up it would be 4a=… And when you use the number given in the equation use the sign given as well… If the “a” value turns out to be positive for a parabola opening down you still have to add the - sign to make it open down)

Question 3

What do you have to put on a parabola graph?

Answer 3

Vertex
Focus
Directrix
Latus Rectum (LR)

Question 4

How do you find the LR?

Answer 4

If it is on the x axis then then the x coordinate is the same as the focus and the y coordinate is 2*a

If it is on the y axis then the y coordinate is the same as the focus and the x coordinate is 2*a

Question 5

How do you find the directrix?

Answer 5

This is the focus but on the opposite side of the vertex

Question 6

What are the equations for parabolas off origin?

Answer 6

(X-h)^2=4a(y-k)
(X-h)^2=-4a(y-k)
(Y-h)^2=4a(x-k)
(Y-h)^2=-4a(x-k)

Question 7

Where is the vertex always going to be?

Answer 7

It will always be between the focus and the directrix

Question 8

What is the distance between the vertex and the focus (or the vertex and the directrix)

Answer 8

The value a

Question 9

When finding the LR what do you do with it when it is off origin?

Answer 9

If it is in the x axis then you either subtract or add to the y coordinate of the focus

If it is in the y-axis then you either subtract or add to the x coordinate of the focus

Question 10

What is the equations for ellipses on the origin?

Answer 10

(X^2/a^2) + (y^2/b^2) = 1
*major axis along x axis

(X^2/b^2) + (y^2/a^2) = 1
*major axis along y axis

Question 11

What is true of a, b, and c

Answer 11

a>b>0

Question 12

What is an equation you have to know to find foci?

Answer 12

b^2=a^2-c^2

Question 13

Helpful hint!!!

Answer 13

a^2 will always be the bigger number when it comes to ellipses.

• Thus if x^2 is above the a^2 then the major axis is the x axis
• if y^2 is above the a^2 then the major axis is the y axis

Question 14

What do you graph when drawing an ellipse?

Answer 14

Center
Two vertex
Two foci
“Vertex” in the minor axis

Question 15

What symbol goes with Focus?

Answer 15

C

Question 16

What letter goes with the vertex?

Answer 16

A

Question 17

What letter goes with the vertex on the MINOR axis?

Answer 17

B

Question 18

What are the equations for ellipses that are off origin?

Answer 18

(X-h)^2/a^2 + (y-k)^2/b^2 =1

(X-h)^2/b^2 + (y-k)^2/a^2 =1

Question 19

Helpful hint #2

Answer 19

Base where the focus are based on where the center and vertex on the major axis are!
In between both of those is where the focus will be!!