# Rectangular and parametric forms of conic sections?

• May 13th 2011, 05:28 PM
homeylova223
Rectangular and parametric forms of conic sections?
Find the rectangular equation of the curve whose parametric equations are given.

1.x=-cost t, y= sin t

2. x=-sin 2t
y=2 cos 2t

Now I am kind of confused what to for with the the "2t"

For example on number 2 I did

2 cos 2t=y
cos2t=y/2 Would I do know square it but while I would get y^2/4 on one side what would I do on the "other side"?(Giggle)
• May 13th 2011, 05:33 PM
TheEmptySet
Quote:

Originally Posted by homeylova223
Find the rectangular equation of the curve whose parametric equations are given.

1.x=-cost t, y= sin t

2. x=-sin 2t
y=2 cos 2t

Now I am kind of confused what to for with the the "2t"

For example on number 2 I did

2 cos 2t=y
cos2t=y/2 Would I do know square it but while I would get y^2/4 on one side what would I do on the "other side"?(Giggle)

You have a good start but you need to keep going and use the Pythagorean identity.

$\sin^2(x)+\cos^2(x)=1$

$(-x)^2+\left( \frac{y}{2}\right)^2=1 \iff x^2+ \frac{y^2}{4}=1$
• May 13th 2011, 05:57 PM
homeylova223
So would the answer to my first question be

(-x)^2+ (y)^2=1
x^2+y^2=1
• May 13th 2011, 06:41 PM
TheEmptySet
Yes