You already know a lot about parabolas from Math 121, so now you just have the added piece of information about the focus and directrix. It shouldn't be too bad, but if you have found a question that you don't think you can answer without the information in the blue box in front of you, post that question and we can see about getting some strategies for thinking about it without the book in front of you.
For hyperbolas and ellipses, rely on the fact that they are very similar to each other. They both have a center (h,k). For both of them we usually use the constant c to represent the length of the center to a focus. We usually use the constant a to represent the length from the center to a vertex. We usually use the constant b, to represent the length from the center to what would be the end points of the minor axis in an ellipse or the top of the box in a hyperbola.
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Notice that the a and b are can be thought of as the same for the hyperbola and the ellipse. In an ellipse c2 + b2 = a2 which can be remembered since a is longer than b and c.
In a hyperbola a2 + b2 = c2 which can be remembered since c is longer than a and b.
What would be different about the hyperbola if we used the same a and b as above, but ... |
Click here to find an explanation of the asymptotes of a hyperbola.
