6-4

This week is a golden opportunity to review hyperbolas. I am sure some of you remember this, but others of you may not so here we go with the blogging and the teaching and what not.

Standard form!

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

1. Major axis is bigger denominator (i.e. positive)

2. Minor axis is smaller denominator (i.e. negative)

3. The vertex is square root of largest denominator (in point form the answer goes in place of the major axis)

4. The other intercept is the square root of the smallest denominator (see above for point form)

Steps 5 and 6 are unnecessary for hyperbolas.

7. f^2=larger denominator+smaller denominator OR f^2=vertex^2+other value^2

8. Asymptotes

y=+/- square root of y denom/square root x denom x

At the end you graph it, but I won't be doing that.

EXAMPLE

-x^2/16+y^2/36=1

1. y is major

2. x is minor

3. square root of 36=6

4. square root of 16=4

5 and 6 are still unnecessary.

7. f^2=16+36

f=square root of 52 or +/-2 square root of 13 (0,2square root 13)(0,-2square root 13)

8. y=+/-6/4= +/-3/2

Don't forget to graph after.

--Sarah