6-4 Hyperbolas

Standard Form of Hyperbolas:

x^2/a^2 -y^2/b^2 =1 or -x^2/a^2+y^2/b^2 =1

The steps for solving a hyperbola are as follows:

1. Identify the major axis which is always the largest denominator.

2. Find the minor axis which is the smallest denominator.

3. Take the square root of the largest denominator and write it in point form (x,y) and (-x,-y)

4. Take the square root of the smallest denominator and write that in point form.

5. To find the focus, one must use the formula f^2 equals largest denominator plus smallest denominator. Write the focus in point form when it's found.

6. To find asymptotes one must use the formula y equals plus or minus the square root of the y denominator over the square root of the x denominator. It is to be written in slope intercept form.

An example of this problem

x^2/81 - y^2/9=1

1. The major axis is x.

2. The minor axis is y.

3. Take the square root of 81 and one will end up with 9. In point form it looks like (9,0) and (-9,0)

4. Take the square root of 9 and one will end up with 3. In point form, it's (0,3) and (0,-3)

5. The focus formula in hyperbolas is focus squared equals largest denominator plus smallest denominator, the f^2= 9 + 81 which makes focus squared equal 90. When you square root both sides you get focus equals the square root of 90 which simplifies to 3 square roots of 10. It goes in point form simplified.

6. The square root of the y denominator (9) is put over the square root of the x denominator(81). The asymptote is placed in slope intercept form as y= +or- 1/9x

And that's the way the cookie crumbles!

-Sameer