## dricboylan 2 years ago What are the vertices of the hyperbola given by the equation (y-4)^2/121 - (x+9)^2/141 = 1?

1. satellite73

first you need the center so you know that one ?

2. dricboylan

No, I really don't understand this section which is why I was asking for help.

3. satellite73

center of $\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$is $$(h,k)$$

4. satellite73

in your case it is $$(-9,4)$$

5. satellite73

because the $$y$$ part comes first (before the minus sign) this hyperbola looks like this (roughly) |dw:1353293873616:dw|

6. satellite73

to find the vertices, go $$a$$ units up up and down from the center. that is why you needed the center first in your case $$a^2=121$$ and so $$a=11$$

7. satellite73

since the center is $$(-9,4)$$ if you go up 11 units you are at $$(-9,15)$$ and if you go down 11 units you are at $$(-9,-7)$$

8. satellite73

hope that is clear, and also that you see it is not that hard once you know what you are doing

9. dricboylan

I'm still extremely lost, as you can tell math isn't my strong point. I appreciate the help however.