Hyperbolas & Identifying graphs

*Standard form
x^2/a^2-y^2/b^2=1

1. the major axis is the variable with the largest denominator (positive)
2. the minor is the variable with the smallest denominator (negative)
3. The vertex is the square root of the largest denominator (put in point form)
4. The other value is the square root of the smallest denominator (put in point form)
5. Skip
6. Skip
7. Focus - F^2=largest denominator + smallest denominator
8. Horizontal Asymptotes - x= + or - square root of y denominator / square root of x denominator 
9. Graph

Ax^2+Bxy+Cy^2+Dx+Ey+F=o *standard form*

-To find the shape of the graph without using the standard form, plug into B^2-4AC

• If it is a circle, you get a negative number,  A=C & B=o
• If it is an ellipse, you get a negative number, A doesn't = C, *& B doesn't = 0
• If it is a parabola you get 0
• If it is a hyperbola, you got a positive number

Example 1: Identify the graph of the equation : X^2-2xy+3y^2-1=0

A=1   B=-2   C=0

B^2-4AC

(-2)^2-4(1)(3)

4-12=-8

Ellipse

1) Take the coefficients of your A, B, & C term

2) Plug them into your formula

3) Solve, then look back at your notes when you find your answer to identify what the graph is