Conic Sections

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

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

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=9 .____ Center (2, -3) radius 3 r

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

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)

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

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)

What conic will the equation create?