Hyperbolas

How to do a Hyperbola:

1. Find whether x or y is the major axis: look for a negative sign. That negative sign will tell you "oh look the minor axis." So that means the other variable is the major axis.
2. Find your minor axis: Was kinda already explained, but look for that negative sign; you will find your minor axis.
3. Find your vertex: (Use your major axis for this) Take the square root of your major axis and put it in point form, also if the major axis is "x", then the answer goes in the x spot for point form (x, ) and if the major axis is "y", then the answer goes in the y spot for point form ( ,y).
4. Find the next value: (Use your minor axis for this) Take the square root of your minor axis and put it in point form (see above).
5. Find your focus: (you can use this to find the vertex or other intercept as well by working backwards) focus^2 = largest denominator + smaller denominator or focus^2 = vertex^2 + other value^2 (In my opinion, it is much easier to use the first one).
6. Find Asymptotes: y = +/- square root of the y denominator devided by the square root of the x denominator times x.
Example of a Hyperbola:
1/2. y^2/16 - x^2/4 = 1
Okay, so by looking at that negative you know that x is your minor axis and y is your major axis.
3. Vertex time, take the square root of 16 and get +/- 4. Point form: (4,0),(-4,0)
4. Other Value, take the square root of 4 and get +/- 2. Point form: (0,2),(0,-2)
5. Focus, focus^2 = 16 + 4 , Focus^2 = 20 and the square root of 20 is 4.4 but you must leave it in radical form so you should get 2square root of 5. Put that in point form and get (2square root of 5, 0), (-2square root of 5,0).
6. Asymptotes, y= +/- the square root of 16 divided by the square root of 4 times x and get y= +/- 4x
7. You have found the equation for the asymptotes and found the point for the Vertex, foci; other values.
8. You would then graph the hyperbola by making a makeshift graph. Plotting the vertex and values on the graph, draw a rectangle connecting the points and then drawing a dotted line through each of the edges of that dotted rectangle. Now plot your hyperbolas on the axis with the largest denominator regardless of whether it is + or - , use the dotted lines that go through the edges of the rectangle for an accurate measurement. Now just use the angled dotted lines that you drew that passes through the origin, (0,0) and through the edges for your asymptotes. For the dotted line going up put y= 4x next to the top right of the line; for the line going down put y=-4x next to the top left of the line.
And there you have it, your hyperbola.