Parametrically Defined Curves

**heatly** · February 22nd 2011, 08:59 PM

Describe the following curve:
r(t)=2cost i +3sint j

The ans is:

An Ellipse
since (x^2)/(2^2)+(y^2)/(3^2) = 1

I cant see where they get this ans from?

**Prove It** · February 22nd 2011, 09:02 PM

$\displaystyle x = 2\cos{t} \implies \cos{t} = \frac{x}{2}$

$\displaystyle y = 3\sin{t} \implies \sin{t} = \frac{y}{3}$ .

$\displaystyle \sin^2{t} + \cos^2{t} = 1$

$\displaystyle \left(\frac{y}{3}\right)^2 + \left(\frac{x}{2}\right)^2 = 1$

$\displaystyle \frac{y^2}{9} + \frac{x^2}{4} = 1$ .

It's an ellipse.

Thread: Parametrically Defined Curves

LinkBack

Thread Tools

Display

Parametrically Defined Curves

Similar Math Help Forum Discussions

parametrically defined curve

In Matlab, how to refer a self-defined function in another self-defined function?

cycloid parametrically and surface area

parametric and implicitly defined curves

sketching curves-transformation curves f(x)!!!!

Search Tags