Hyperbolas (Horizontal)

Write a rule describing how to find the vertices of the hyperbola if the center of the hyperbola is (h,k).

Write a rule describing how to find the foci of the hyperbola if the center of the hyperbola is (h,k).

What is the distance between the two vertices? Between the two foci?

There are slant asymptotes that can be drawn that the two branches of the hyperbola get close to, but never actually touch. Find the slope of these asymptotes in terms of a and b. (Hint: for an example, let a=2 and b=3. What is the slope of both asymptotes?)

Now that you have the slopes of the slant asymptotes, write the equation of the lines. Your equation should include b, a, h, and k. (Hint: for an example, let a=2 and b=3 as before, and let h=1 and k=-3. What are the equations of those lines? You may need to recall how to perform a transformation, specifically, a translation, on a function.)

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

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

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