How do you identity if the equation #3x^2-2y^2+32y-134=0# is a parabola, circle, ellipse, or hyperbola and how do you graph it?
This is a hyperbola! noticing the negative
This is a hyperbola in the general form, which means you must complete the square before graphing.
This is the standard form for a hyperbolic graph, because it is of the form:
Of course, in this case
The formula for the two oblique asymptotes are given by:
Now you can sketch the two asymptotes on the plane.
After this, we must find any x- and y-intercepts, simply by letting one or the other equal zero.
Now you are ready to sketch this hyperbola. Remember not to direct the curve away from the asymptote as it approaches it.