Exam 3 Flashcards
Rectangular coordinates (x,y)
costheta = x/r
sintheta = y/r
x^2+y^2=r^2
Polar coordinates (r, theta)
x = rcostheta y = rsintheta tantheta = y/x theta = tan^-1(y/x)
Circles
x^2+y^2 = a^2 r = a (center) x^2+y^2 = +-2ax (x-axis) x^2+y^2 = +-2ay (y-axis)
Cardioid
r = a+acostheta or a+asintheta a/a = 1
Limacon without inner loop
r = a+b costheta or a+b sin theta
0<b>1</b>
Limacon with an inner loop
r = a+b costheta or a+b sin theta
0<a></a>
Lemniscate
r^2 = a^2cos(2theta) r^2 = a^2sin (2theta)
Rose with three petals
r = asin(3theta) or acos(3theta)
Rose with four petals
r = asin(2theta) or acos(2theta)
Ellipses
(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
Hyperbolas
(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)
Parabolas (vertical facing left)
v = (0,0)
f = (a,0)
d: x = -a
e: y^2 = 4ax
Parabolas (vertical facing right)
v = (0,0)
f = (-a,0)
d: x = a
e: y^2 = -4ax
Parabolas (horizontal facing up)
v = (0,0)
f = (0, a)
d: y = -a
e: x^2 = 4ay
Parabolas (horizontal facing down)
v = (0,0)
f = (0, -a)
d: y = a
e: x^2 = -4ay
r = ep/1-ecostheta
D: perpendicular
p units distant
Left side of the pole
r = ep/1+ecostheta
D: perpendicular
p units distant
Right side of the pole
r = ep/1-esintheta
D: parallel
p units distant
Below the pole
r = ep/1+esintheta
D: parallel
p units distant
Above the pole
Parabola (conic)
e = 1
Hyperbola (conic)
e > 1
Ellipse (conic)
e < 1
Vector starting at P = x1, y2 and ending at Q = x2,y2
w = (x2-x1)i + (y2-y1)j w = ai+bj
v = a1i+b1j
||v|| = sqrt of a1^2 + b1^2
