Sketch the graph of x^2 - y^2 = 16
Before attempting to re-arrange the equation, we take an organic approach to looking at asymptotes:1) What happens to y when x=0 and when x -> infinity? What happens to x when y=0 and when y -> infinity?2) We establish the coordinates (4,0) and (-4,0), as well as the odd behaviour at at x=y and -x=-y, which the student may or may not notice are asymptotes. 3) We attempt to draw the graph – which can be made even easier by considering adjacent points to the coordinates we know.
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