Question

Eliminate the parameter.

x = 3 cos t, y = 3 sin t

Answer 1

So far I have:

x/3 = cos(t)
and
y/3 = sin(t)

then
(y/3)^2 + (x/3)^2 = 1

but in the example in my lesson, it went a step further and squared out the demoninators which would make this answer:

((y^2)/9) + ((x^2)/9) = 1

is that what I should do for this? And then should I add them because of like terms? or no?

Answer 2

The lesson said that it did that because it made it into the standard form of an ellipse. does this apply here, or is the regular answer correct?

Answer 3

correct

Answer 4

So the answer would simply be:

(y/3)^2 + (x/3)^2 = 1

right?

Answer 5

should be under the form of
\[\dfrac{x^2}{9}+\dfrac{y^2}{9}=1\]

Answer 6

oh, okay. so you do square out the denominators. Does this put this answer in the standard form of an ellipse?

Answer 7

if you define it is a ellipse, it is so.
however, I would like to say it is a circle (x^2+y^2 =9)

Answer 8

oh okay. My lesson just referred to it as an ellipse.

Thanks!!