Question
Find a parametric equation for the ellipse. Make sure that the graph of your parametric equation is a complete ellipse.
3x^2+4y^2=12
3x^2+4y^2=12
Answers
Reiny
3x^2 + 4y^2 = 12
divide by 12
x^2/4 + y^2/3 = 1
we know sin^2 t + cos^2 t = 1
so sin^2 t = x^2/4 = (x/2)^2
---> sin t x/s ----> x = 2sin t
and
cos^2 t = y^2/3 = (y/√3)^2
cos t = y/√3
----> y = √3cos t
x = 2sint
y = √4cost
confirmation:
http://www.wolframalpha.com/input/?i=x+%3D+2sint+%2C+y+%3D+√3cost
divide by 12
x^2/4 + y^2/3 = 1
we know sin^2 t + cos^2 t = 1
so sin^2 t = x^2/4 = (x/2)^2
---> sin t x/s ----> x = 2sin t
and
cos^2 t = y^2/3 = (y/√3)^2
cos t = y/√3
----> y = √3cos t
x = 2sint
y = √4cost
confirmation:
http://www.wolframalpha.com/input/?i=x+%3D+2sint+%2C+y+%3D+√3cost