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Level 533

Parametric Equations


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(r, θ)
polar coordinates
(x, y)
Rectangular Form (Coordinates)
rcosθ=x
Equations to convert polar to rectangular (and vice versa)
y=t
Equations to convert rectangular to parametric
Substitution/trig identites
Equations to convert parametric to rectangular
x=rcosθ
Equations to convert polar to parametric
r=ro+tm = <x,y,z>+t<x,y,z>
vector equation of a line
x(t)=? y(t)=? z(x)=?
parametric equation of a line
x²+y²=4
x=2sint y=2cost
y=(x/2)+6
x=2t y=t+6
y=x²-1
x=sect y=tan²t
r=-4cosθ
x= -2 + 2cosθ
r=<2-t,4+5t,-3-4t>
Find the vector equation and the parametric equations of the line that passes through points (2, 4, -3) and (3, -1, 1). At what points does the line intersect the x, y, and z planes.
x(t)= -t y(t)=1+2t z(t)=5+7t
Find the parametric equations of the line of intersection of the planes: 2x+y=1 and x-3y+z=2
r=<-2 + 2t, 4 - 4t,10 + 5t>
Find a vector equation and parametric equations for the line through the point (-2, 4, 10) and parallel to the vector: v= 2i −4j +5k .
x=e∧t y=e∧-t
[r² = 2 csc 2θ] [xy = 1; x > 0] [x = e∧t y = e∧-t; x & y > 0]
y=(5/3)x
Find a vector equation and parametric equations for the curve by eliminating the parameter: x=3t, y=5t
r=<3t, 4+2t, -3+t>
Find a vector equation and parametric equations for the line through the point (0, 4, -3) and perpendicular to the plane: 3x+2y+z=2