Question

write the equation of an ellipse with minor axis of length 8 and vertices at (-9,3) and (7,3)

Answer 1

The minor axis = 8 tells you that 2b=8

Answer 2

Can you find the distance from (-9,3) to (7,3)? That distance is the length of the major axis which is 2a

Answer 3

its 17 units away

Answer 4

From (-9,3) to (7,3) is 16

Answer 5

The center is the midpoint of the major axis.

Answer 6

so 16 is the midpoint?

Answer 7

The length of the major axis is 16

Answer 8

Do you know how to find a midpoint?

Answer 9

no not at all

Answer 10

Add the x coordinates and divide by 2. Add the y coordinates and divide by 2. That will give you the midpoint.

Answer 11

\[x=\frac{x _{1}+x _{2}}{2}\]

Answer 12

\[y=\frac{y _{1}+y _{2}}{2}\]

Answer 13

I got -1,3

Answer 14

Yes. That is the center.

Answer 15

Now you just need to plug into the equation of an ellipse:

Answer 16

\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\]

Answer 17

(h,k) is the center.

Answer 18

what would x and y be?

Answer 19

@Mertsj

Answer 20

x and y remain in the equation.

Answer 21

ok does a^2 and b^2 stay the same or no?

Answer 22

Replace a and b with the values you calculated.

Answer 23

-1,3 again?

Answer 24

2b=8

Answer 25

Can you find the distance from (-9,3) to (7,3)? That distance is the length of the major axis which is 2a

Answer 26

that 16

Answer 27

*thats

Answer 28

Yes. 2a = 16

Answer 29

b^2 is 8 and a^2 is 16

Answer 30

2b=8
Solve for b

Answer 31

Yes. 2a = 16
Solve for a

Answer 32

its 4

Answer 33

If b = 4, what is b^2?

Answer 34

I'm not really sure

Answer 35

What class are you taking?

Answer 36

alg. 2 I just dont know this chapter well

Answer 37

How is it you don't know how to raise a number to the second power?

Answer 38

o well 2 to the second power is 4 if that what your asking

Answer 39

You said that b = 4 and that is correct. I then asked, "what is b^2?" You said you didn't know.

Answer 40

I thought you want the square root of 16 thats why or what can go into 8 and 2

Answer 41

What is a?

Answer 42

I pretty sure its 4 because of 16

Answer 43

2a = 16 Solve for a

Answer 44

I'm not sure what it is I confused

Answer 45

i'm *

Answer 46

So you are telling me that you are in Algebra II, studying ellipses and you cannot solve this equation: