How Do Lines Intersect with a Hyperbola in Different Ways?

[Cacophony]

Homework Statement

Hello all, I am searching for help with conic intersections and i have a question I would like to ask.

-Consider the hyperbola x^2-y^2 = 1. A line in R^2 (All real numbers squared) can intersect this hyperbola in one of four ways: not at all, at one point crossing the hyperbola, at one point tangent to the hyperbola, and at two points. For each of the four cases, find a line which is an example of that case.

I've been doing some conic intersection example and am starting to understand the basic to intermediate stuff. However, I have no idea where to start with this one. Would someone please give me some pointers?

Homework Equations

The Attempt at a Solution

 

[xaos]

"A line in R^2 (All real numbers squared) "

R^2 is usually thought of as the space of all points (x,y), not the set of all squared numbers, so the equation of the line in the plane R^2 is ax+by=c.