Question

How do you graph `(x^2 / 4) - (y^2 / 9) =1`?

Answer 1

This hyperbola will open East-West and be centered at the origin.

Explanation:

You will move right and left 2 units from center to find the vertices. This comes from `sqrt(4)` that is the denominator of the `x^2` term.

Then, go up and down 3 units (`sqrt(9)`) to find corners of a "box" that will create asymptotes for your shape. The slopes of the asymptotes will be `+-3/2` for these reasons.

This graph was created in TI-nspire, with a template for graphing the conic sections and other relations. I didn't plot any points except for the vertices at (2,0) and (-2,0). If you are required to have more precision, make a table for ordered pairs.