precal stuf

parametric of a line

x\=x1+t(x2-x1) and y\=y1+t(y2-y1)

parametric of a circle

x\=h+rcost
y\=k+rsint

parametric of a horizontal ellipse

x\=h+acost and y\=k+bsint

parametric of a vertical ellipse

x\=h+acost and y\=k+asint

parametric of a horizontal hyperbola

x\=h+asect and y\=k+btant

parametric of a vertical hyperbola

x\=h+btant and y\=k+asect

motion x(t)

v0tcost+_wind*t

motion y(t)

v0tsint-16t^2+s0

when do you use s(t)?

when an object is thrown straight up

s(t)

-16t^2+v0t+s0

standard eq of a vertical parabola

(x-h)^2\=4p(y-k)

standard eq of a horizontal parabola

(y-k)^2\=4p(x-h)

standard eq of a horizontal ellipse

(x-h)^2/a^2+(y-k)^2/b^2\=1

standard eq of a vertical ellipse

(x-h)^2/b^2+(y-k)^2/a^2\=1

e\=

c/a

how to find c of an ellipse

a^2-b^2\=c^2

standard eq of a horizontal hyperbola

(x-h)^2/a^2-(y-k)^2/b^2\=1

how to find c of a hyperbola

c²\=a²+b²

standard eq of a vertical hyperbola

(y-k)^2/a^2-(x-h)^2/b^2\=1

eq of asymptote for a horizontal hyperbola

y\=k+_b/a(x-h)

eq of asymptote for a vertical hyperbola

y\=k+_a/b(x-h)

if the eccentricity of a hyperbola is large, the branches are \______

nearly flat

if the eccentricity of a hyperbola is close to one, the branches are \_______

more narrow

if the discriminant of a conic is

ellipse or circle

if the discriminant of a conic is \=0, it is a...

parabola

if the discriminant of a conic is \>0, it is a...

hyperbola

formula to find rotation angle (in deg)

cot2t\=(A-C)/B

if you're using a calculator that does not have inverse cot, what do you do?

switch to inverse tan, if 2t is less than 0, add 180 and div by 2