Flashcards in Parametric Equations Deck (18):

1

## Parametric curve

### A set of points generated by a parametric equation

2

## Parameter

### The third variable, usually 't' upon which the independent or dependent variable depends

3

## Forward orientaion

### The direction in which the curve is generated as the parameter increases

4

## Derivatives of Parametric curves

###
Written as [dy/dt]/[dx/dt]

h'(t)/g'(t)

h(t)- function that outputs the y-value

g(t)- function that outputs the x-value

5

## Parametric equations for an ellipse/circle

###
x(θ)=cos(θ)*'r'

y(θ)=sin(θ)*'r'

6

## Parametric equations for a hyperbola

###
x(θ)=sec(θ)*'r'

y(θ)=tan(θ)*'b'

b= √(c^2-a^2)

a= vertices of (0,±a) or (±a,0)

c= foci at (0,±a) or (±a,0)

7

## Parametric equations for a parabola

###
x(θ)=2θ*r

y(θ)=θ^2*r

8

## Parametric equations in colloidal dispersion/concentration

### S

9

## Translations and rotations of axis

### A

10

## Celestial orbit in Parametric equations

### S

11

## Length of the polar curve

### L= ∫ √(f(θ)^2+f'(θ)^2)dθ

12

## Arc Length with time

###
s(t)=∫|v(u)|du

from a to t

13

## Curvature

###
How much the tangent vector changes given time

14

## Curvature (given arc-length)

### k=|d(r'/|r'|)/ds|

15

## Curvature (given time)

###
k=|d(r'/|r'|)/dt|/|v|

Also

=|T'(t)/r'(t)|

16

## Curvature (given a point)

### k=(r"xr')/(|v|^3)

17

## T-value of parametric equations

### T=(r'/|r'|)

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