Thread: Parametric equation of an ellipse

Can somebody please help me if the following is correct:

I must give parametric equations for the following ellipses:

1) 3x^2 + 5y^2 = 75

Since a=5 and b=sqrt(15), is this my correct answer:
x = 5 cos t
y = sqrt(15) sin t

2) 3x^2 + 12x + 5y^2 -10y -58 =0

Since a=5 and b=sqrt(15) like above mentioned, but this ellipse is transformed so that the new center became (-2, 1), then is it that the parametric equations became:
x= -2 + (5 cos t)
y= 1 + (sqrt(15) sin t)

Many thanks to someone who helps!
Brigitte

I got the same answers, so your answers look correct to me

Originally Posted by dolkam

Can somebody please help me if the following is correct:

I must give parametric equations for the following ellipses:

1) 3x^2 + 5y^2 = 75

Since a=5 and b=sqrt(15), is this my correct answer:
x = 5 cos t
y = sqrt(15) sin t

2) 3x^2 + 12x + 5y^2 -10y -58 =0

Since a=5 and b=sqrt(15) like above mentioned, but this ellipse is transformed so that the new center became (-2, 1), then is it that the parametric equations became:
x= -2 + (5 cos t)
y= 1 + (sqrt(15) sin t)

Many thanks to someone who helps!
Brigitte

You should be checking your answer by substituting the parametric equation into the cartesian ones. They are both correct.


Subbing in and






Subbing in and

Thank you very much.

I did not think about the substituting into the cartesian.

I will do that.

Brigitte