Expert: Sherry Wallin - 3/20/2009

Question
For what value(s) of a does the system of equations

(i) x^2 = y^2
(ii) (x - a)^2 + y^2 = 1

i cant figure out if x^2 = y^2 is a hyperbola

pls help me


Answer
Nickson~
    Try plotting several points for x^2 = y^2. Let's see when x = 0, y = 0. When x = 1 then y = 1. Suppose x = -1, then x^2 = (-1)^2 = 1. What points did you generate? (0,0), (1,1),(-1,1) and so on, this looks to me like the absolute value function, what do you think? Here the assumption is that y is the dependent variable. A hyperbola needs to be able to be written as x^2/a^2  - y^2/b^2 = 1. Here you have x^2-y^2 = 0 and a = b = 1. You will never get the right hand side to be equal to 1, that is why it is not a *hyperbola*.

Math Prof