Distance and Midpoint Formulas The distance d between the points (x 1, y 1 ) and (x 2, y 2 ) is given by the distance formula: The coordinates of the point halfway between the points (x 1, y 1 ) and (x 2, y 2 ) is given by the midpoint formula: (x 1, y 1 ) (x 2, y 2 )

Conics Parabolas Equations of parabolas are quadratic in x or y Vertex at (0, 0) Vertex at (h, k)

Conics Parabolas If the x term is quadratic, (ax 2 ), the parabola is vertical. If a > 0, it opens up If a < 0, it opens down

Conics Parabolas If the y term is quadratic, (ay 2 ), the parabola is horizontal. If a > 0, it opens right If a < 0, it opens left

Conics Circles and Ellipses Standard form for an ellipse centered at origin: -a a -b b

Conics Circles and Ellipses Standard form for a circle centered at origin with radius r: r-r r

Conics Hyperbolas Standard form for hyperbolas centered at origin: -aa b -b

Conics If the curve is centered at (h,k), replace the x in the equation with x-h and replace the y with y-k.