## anonymous one year ago Can someone help me with two questions in conic sections.

1. anonymous

1. What is the equation of the following graph?

2. anonymous

2. What are the foci of the following graph?

3. xapproachesinfinity

i hyperbola has the equation $$\Large \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$ so you need to find a and b

4. anonymous

how do I find a and b?

5. xapproachesinfinity

you see that box a is half way from right to left b is half way from bottom up

6. xapproachesinfinity

so you just take the length of that rectangle and divide into half

7. xapproachesinfinity

2b=8 so b=4 2a=6 so a=3

8. anonymous

okay thank you! so the first problem is $\frac{ x ^{2} }{ 3^{2} }-\frac{ y ^{2} }{ 4^{2} }=1$

9. xapproachesinfinity

yes !

10. anonymous

Can you also help with the 2nd problem

11. xapproachesinfinity

to find the foci you need to find a and b again then use b^2+c^2=a^2 c=sqrt{a^2-b^2} c is the distance from the foci to the center of that rectangle

12. xapproachesinfinity

that will get you the coordinates of the foci

13. xapproachesinfinity

you will find b and a the same way we just did

14. anonymous

I got A=2 and B=5 is that correct?

15. xapproachesinfinity

yes!

16. anonymous

okay what do I do next?

17. xapproachesinfinity

well i said c is the distance from center to foci so what do you think any idea

18. xapproachesinfinity

actually an error $$c=\sqrt{a^2+b^2}=\sqrt{29}$$ the foci has coordinates (0,c)

19. anonymous

so c=5.39?