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 cos2t + sin2t = 1
which gives
x2 / 62 + y2 / (sqrt 11)2 = 1 . . . . . . . .
er! how does this happen, if you could help!
Re: Conics: ellipse in standard position
, \ y = \sqrt{11}\sin(t))
, so
 = \frac{x}{6}, \ \sin(t) = \frac{y}{\sqrt{11}})
, so
 = \left(\frac{x}{6}\right)^2, \ \sin^2(t) = \left(\frac{y}{\sqrt{11}}\right)^2)
, so
 = \frac{x^2}{6^2}, \ \sin^2(t) = \frac{y^2}{(\sqrt{11})^2})
.
NOW, use the trigonometry formula  + \sin^2(t) = 1)
, and plug in what we just found.
, so
 + \left( \frac{y^2}{(\sqrt{11})^2} \right) = 1)
, so
^2} = 1)
.
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. :-)
