Hyperbolas (Vertical)

Question 1

How do you determine the center of the hyperbola?

Question 2

Write a rule describing how to find the vertices of the hyperbola based on your coordinates in question 1.

Question 3

Write a rule describing how to find the foci of the hyperbola based on your coordinates in question 1.

Question 4

Just like the horizontal hyperbola, the branches of the vertical hyperbola get close to, but never actually touch the slant asymptotes. Determine the equations of these two lines.

Question 5

What is the equation of the hyperbola in "Hyperbola Equation #1"?

[math]\frac{\left(y-3\right)^2}{4}-\frac{\left(x+2\right)^2}{16}=1[/math] [math]\frac{\left(y+3\right)^2}{16}-\frac{\left(x-2\right)^2}{4}=1[/math] [math]\frac{\left(y-3\right)^2}{4}+\frac{\left(x+2\right)^2}{16}=1[/math] [math]\frac{\left(y+3\right)^2}{4}-\frac{\left(x-2\right)^2}{16}=1[/math]

Question 6

What are the slopes of the asymptotes in "Hyperbola Equation #1"?

[math]\pm\frac{1}{2}[/math] [math]\pm\frac{3}{2}[/math] [math]\pm2[/math] [math]\pm\frac{2}{3}[/math]

Question 7

Determine the equation of the hyperbola in "Hyperbola Equation #2." Also, give the equations of the asymptotes.