Distance and Midpoint Formulas

The distance d between the points (x1, y1) and (x2, y2) is given by the distance formula:

2122

12 yyxxd

The coordinates of the point halfway between the points (x1, y1) and (x2, y2) is given by the midpoint formula:

222121 yy

,xx

• (x1, y1)

• (x2, y2)

•

Conics

Parabolas

Equations of parabolas are quadratic in x or y

2

2

ayx

axy

Vertex at (0, 0)

2

2

kyahx

hxaky

Vertex at (h, k)

Conics

Parabolas

If the x term is quadratic, (ax2), the parabola is vertical.

If a > 0, it opens up

If a < 0, it opens down

Conics

Parabolas

If the y term is quadratic, (ay2), 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:

12

2

2

2

b

y

a

x

-a a

-b

b

Conics

Circles and Ellipses

Standard form for a circle centered at origin with radius r:

222 ryx r-r

r

-r

ConicsHyperbolas

Standard form for hyperbolas centered at origin:

12

2

2

2

b

y

a

x

-a a

12

2

2

2

a

x

b

yb

-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.

222 rkyhx

12

2

2

2

b

ky

a

hx

12

2

2

2

a

hx

b

ky 12

2

2

2

b

ky

a

hx