Parametric Equations

Question 1

Sketching a curve

Answer 1

Create the table
Solve for t in one equation
Substitute that for t in a different equation
result is rectangular equation
find x and y

Question 2

Curve with sin and cos

Answer 2

Plug in angle measures
Get sin and cos by themselves
Convert to ellipse form with the numbers squared on the bottom

Question 3

Given points line

Answer 3

Use the equation
x= x1+t(x2-x1)
y=y1+t(y2-y1)

Question 4

Given center and radius circle

Answer 4

Use x=h+rcos(theta)
y=k+rain(theta)

Question 5

Ellipse given vertices and foci

Answer 5

Find center
Find a (distance from center to vertex)
Find b with a^2+b^2=c^2
If its horizontal use
x=h+acos(theta)
y=k+bsin(theta)

if vertical use
x=h+bcos(theta)
y=k+asin(theta)

Question 6

how to find the time given feet away and height

Answer 6

plug feet away into x and solve for t