## briana.img one year ago How do you write an equation for a hyperbola that involves foci?

1. briana.img

2. briana.img

3. jim_thompson5910

|dw:1435360080154:dw|

4. jim_thompson5910

Foci |dw:1435360096843:dw|

5. jim_thompson5910

vertices |dw:1435360133480:dw|

6. jim_thompson5910

what is the midpoint of the vertices? |dw:1435360163097:dw|

7. briana.img

(4,0) ???

8. jim_thompson5910

4 is correct 0 is not

9. briana.img

(4,5)

10. jim_thompson5910

good

11. jim_thompson5910

|dw:1435360285728:dw|

12. jim_thompson5910

The distance from the center to either vertex is what numeric value?

13. briana.img

Ok I understand that the top half of the equation with be (x-4)^2 - (y-5)^2

14. jim_thompson5910

correct

15. briana.img

The distance from either vertex is two?

16. jim_thompson5910

from center to vertex (pick one) is 2 units, yes

17. jim_thompson5910

so a = 2 where $\Large \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$

18. jim_thompson5910

'a' corresponds to the x portion because the hyperbola opens along the x axis direction (ie horizontally)

19. jim_thompson5910

c = 3 because it is 3 units from the center to either focus use a^2 + b^2 = c^2 to find b

20. jim_thompson5910

actually you don't need to solve for b you can stop at b^2 and that would be fine too

21. briana.img

@jim_thompson5910 oh okay! i clearly understand now!! thank you :)

22. jim_thompson5910

no problem