Hyperbola

This week we learned about hyperbola's as part of chapter six. The standard form for a hyperbola could be x^2/a^2-y^2/b^2=1 or -x^2/a^2+y^2/b^2=1.

1. The largest denominator is the variable that is positive.

2. The smallest denominator is the variable that is negative.

3. To find the vertex you square root the largest denominator then put in point form.

4. Square root the smallest denominator to find the other value but pay no attention to the negative.

5.&6. We do not do these steps for this section.

7. To find the focus or denominator use the formula: focus^2=largest den.+smallest den. Or focus^2=vertex^2+other value^2

8. To find the horizontal asymptote use the formula y=+/- square root of y den. Over the square root of x den. X

Example. X^2/25-y^2/4=1

1. X is major
2. Y is minor
3. Square root of 25 is +/-5 (5,0) (-5,0)
4. Square root of 4 is +/-2 (0,2) (0,-2)
7. Focus^2=25+4
F=+/- square root of 29. (square root of 29,0) (-square root of 29,0)
8. Horizontal asymptote: y=square root of 4/square root of 25 x
y= +/-2/5x