I have a problem that seems easy enough but i cant seem to find x and y
Problem: find a Parametrization for the graph of the function
Starting at (3,9) and moving towards the origin,using angle
in the accompanying figure as a parameter.
I drew out the graph and took a picture of it and i will include it.
I think i use
Im not sure how to finish solving for x then to solve for y?
Im not sure if i need to find since the slop comes out as zero?
Thank you..
I think you may be confusing the idea of a polar function with the parameteric representation of a function.
Given any function we can always parameterize it with the trivial parmatereization
where t is the parameter.
They asked you to parameterize with respect to the angle so we know that
this gives
where theta is the parameter.
You can use the pythagorean theorem to solve the above relationship (or just draw a triangle).
and solving this system gives
Here is a plot of the parameterization
plot[ x=3sqrt(10)cos(t), y=90cos^2(t)] - Wolfram|Alpha
Okay, notice we are doing the exact same thing!
Now if I divide equation 2 by equation 1 I get
The two starting points are the same.
If you use the 2nd defintion then
and
This gives another paramterization of the parabola.
Remember that there are many different ways to parameterize a curve.
Ok, in the first equation you get an = x i can see how you got that but what is that value? thats not merely the x coordinate is it?
Then, in the second equation has me confused. Where did you get
Not sure how you got the denominator or the answer square root y
Can you explain a little better. Sorry =(