Conics: ellipse in standard position

An example with answer I have goes;

x = 6 cos t

y = sqrt 11 sin t

Write down the equation of the conic & state what type of conic it is.

trig identity cos^{2}t + sin^{2}t = 1

which gives

x^{2} / 6^{2} + y^{2} / (sqrt 11)^{2} = 1 . . . . . . . .

er! how does this happen, if you could help!

Re: Conics: ellipse in standard position

, so

, so

, so

.

NOW, use the trigonometry formula , and plug in what we just found.

, so

, so

.

You could rewrite that as:

.

Did that help?

Re: Conics: ellipse in standard position

A simple answer for a simple problem - thank you for taking the time. :-)