1. Conic Sections

2. Parabola Will have only one variable squared
y=+x2 x=+y2
y=-x2 x=- y2

3. Parabola Non squared term needs to be by itself and postive
x=a(y-k)2+h y=a(x-h)2+k
Vertex for both forms (h, k)
May need to complete the square to get into this form

4. Circle Will have both variables squared, added and with the same coefficients
(x-h)2 + (y-k)2=r2
Center (h, k)
Radius r (h,k)
(x-2)2 + (y+3)2= ____
Center (2, -3) radius r

5. Ellipse Will have both variables squared, added and with different coefficients. Always equals 1.
Center = (h, k)
Move right and left of center point
Move up and down of center point
a2 > b2
b2 > a2

6. Ellipse If not equal to 1 divide entire equation by constant
May need to complete the square to get into standard form (could be x, y or both)

7. Hyperbola Will have both variables squared and subtracted
Hyperbola Will have both variables squared and subtracted. Always equals 1.
Asymptote slope

8. Hyperbola
If not equal to one divide by constant (refer to ellipse example)
May need to complete the square to get into standard form (could be x, y or both)

9. What conic will the equation create?