Thread: Rectangular and parametric forms of conic sections?

1. 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"?

2. 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"?
You have a good start but you need to keep going and use the Pythagorean identity.

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

$\displaystyle (-x)^2+\left( \frac{y}{2}\right)^2=1 \iff x^2+ \frac{y^2}{4}=1$

3. So would the answer to my first question be

(-x)^2+ (y)^2=1
x^2+y^2=1

4. Yes