## briana.img one year ago What are the foci of the following graph?

1. briana.img

2. briana.img

I started with a=1 and b=2 and so c^2=1^2-2^2 it ends up to be c^2=-3 but i don't feel as that's right

3. Loser66

Look at the graph, we can see that the foci must be on the x-axis, hence, the coordinate must be under the form of (-x,0) and (x,0). Therefore, we can get rid of A and D

4. Loser66

Now, if it is B, the point $$(1+\sqrt 3,0)$$ has x-coordinate >1, that is it is out of the graph --> cannot be a foci. Now, we have just.......??

5. briana.img

@Loser66 just C left

6. Loser66

Yup, but does it make sense to you?

7. briana.img

@Loser66 yeah i'll look at this next time i'm having trouble

8. dan815

do you know what is special about the foci

9. Loser66

@dan815 Yes, I do. However, in this case, it is easier than the traditional way on finding the foci out by rejecting the wrong one.

10. dan815

|dw:1435322594474:dw|

11. dan815

|dw:1435322627563:dw|

12. dan815

if you draw a straight line from one foci to another foci while hitting the ellipse anywhere once, the length of the lines forces is constant, using that we can figure out where a foci is for any ellipsode with a and b, dominant and codominant axis respectively

13. dan815

|dw:1435322824510:dw|

14. dan815

|dw:1435322927884:dw|

15. dan815

|dw:1435322980864:dw|

16. dan815

|dw:1435323122841:dw|

17. dan815

|dw:1435323133713:dw|