anonymous one year ago How would I solve this?

1. anonymous

2. Jhannybean

$\large \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} \longrightarrow \frac{(x-(-4))^2}{3^2} -\frac{(y-(-3))^2}{4^2}=1$

3. Jhannybean

On the left you have the equation of a hyperbola, and the right arrow is what the equation of the hyperbola translates into, which is your function

4. Jhannybean

To find the foci and vertices, we need to identify what the center is. center : $$(h,k)$$

5. anonymous

That's wrong, sorry.

6. anonymous

hmm

7. Jhannybean

?...

8. anonymous

-4,-3

9. Jhannybean

Good.

10. Jhannybean

Now the foci lie along the horizontal transverse axis, what you know as the major axis. Therefore to find their location, we use the formula $(h+c),k ~,~ (h-c),k~~, c^2=a^2+b^2 \longrightarrow c=\sqrt{a^2+b^2}$

11. anonymous

c=5

12. anonymous

(1, -3,) (-9,-3)

13. Jhannybean

To find the vertices, you use the equation ${(h+a),k} ~,~ {(h-a),k}$

14. anonymous

(-1, -3) (-7,-3)

15. anonymous

?

16. Jhannybean

Yes, c = 5. You are right.

17. anonymous

Thank you, could you help me with one more?

18. Jhannybean

Sure, i can try

19. anonymous

Thanks :) This is like the opposite I guess.

20. anonymous

@Jhannybean