Exam 3 Flashcards
1
Q
Rectangular coordinates (x,y)
A
costheta = x/r
sintheta = y/r
x^2+y^2=r^2
2
Q
Polar coordinates (r, theta)
A
x = rcostheta y = rsintheta tantheta = y/x theta = tan^-1(y/x)
3
Q
Circles
A
x^2+y^2 = a^2 r = a (center) x^2+y^2 = +-2ax (x-axis) x^2+y^2 = +-2ay (y-axis)
4
Q
Cardioid
A
r = a+acostheta or a+asintheta a/a = 1
5
Q
Limacon without inner loop
A
r = a+b costheta or a+b sin theta
0<b>1</b>
6
Q
Limacon with an inner loop
A
r = a+b costheta or a+b sin theta
0<a></a>
7
Q
Lemniscate
A
r^2 = a^2cos(2theta) r^2 = a^2sin (2theta)
8
Q
Rose with three petals
A
r = asin(3theta) or acos(3theta)
9
Q
Rose with four petals
A
r = asin(2theta) or acos(2theta)
10
Q
Ellipses
A
(x-h)^2/a^2 + (y-k)^2/b^2 = 1 center (h,k) vertices (h+a,k) or (h, a+k) focus (h+c,k) or (h, c+k) c^2 = a^2 - b^2
11
Q
Hyperbolas
A
(x-h)^2/a^2-(y-k)^2/b^2 = 1 c^2 = a^2+b^2 focus = (c,0) or (0,c) vertices = (a,0) or (0,a)
12
Q
Parabolas (vertical facing left)
A
v = (0,0)
f = (a,0)
d: x = -a
e: y^2 = 4ax
13
Q
Parabolas (vertical facing right)
A
v = (0,0)
f = (-a,0)
d: x = a
e: y^2 = -4ax
14
Q
Parabolas (horizontal facing up)
A
v = (0,0)
f = (0, a)
d: y = -a
e: x^2 = 4ay
15
Q
Parabolas (horizontal facing down)
A
v = (0,0)
f = (0, -a)
d: y = a
e: x^2 = -4ay
