Finding a Vector Valued Function for a Curve: Counterwise/Clockwise

[brad sue]

Hi,
I do not know how to do this exercise:
Find a vector valued function f that traces out the given curve in the indicated direction.

4x²+9y²=36. a- Counterwise b- clockwise

Thanks

 

[quasar987]

Hi brad,

Here's an idea: First rewrite the equation (which is probably one of an ellipse) as (2x)² + (3y)² = 6². This strangely resembles the equation of a circle. In fact, if we perform the changes of variable w = 2x and z = 3y, then the equation (2x)² + (3y)² = 6² <==> w² + z² = 6² is that of a circle of radius 6 in the w-z plane. You know how to parametrize a circle, right? Then do so and then change back to the variables x & y to find the corresponding parametrisation in the x-y plane.

 

[Townsend]

In case you don't remember the parametric equations of a circle are

x=a*cos(t)
y=a*sin(t)

Where a is the radius and as t increase in the positive direction the circle is traced out in a counter-clockwise direction...

With that and the information quasar987 gave you, you should be able to figure out what to do...

Good luck

 

[brad sue]

In case you don't remember the parametric equations of a circle are

x=a*cos(t)
y=a*sin(t)

Where a is the radius and as t increase in the positive direction the circle is traced out in a counter-clockwise direction...

With that and the information quasar987 gave you, you should be able to figure out what to do...

Good luck

Thanks to you both