Finding the major and minor axis of ellipse

[yungman]

An ellipse is represented by \rho(t)^2=x^2(t) + y^2(t) where \rho(t) is the distance from origin to the ellipse at a given time.

The way the article used to find the major and minor axis is the take the derivative \frac{d(\rho^2(t))}{d t}=0 to find the maximum and minimum.

My question is why it use \frac{d(\rho^2(t))}{d t}=0, not \frac{d\rho(t)}{d t}=0?

 

[D H]

My question is why it use \frac{d(\rho^2(t))}{d t}=0, not \frac{d\rho(t)}{d t}=0?

Because it's easier and yields the same answers so long as ρ is never 0.

 

[yungman]

Because it's easier and yields the same answers so long as ρ is never 0.

Thanks, so all it is, is to avoid dealing with the square root x^2 + y^2?

 

[D H]

That's all it is. Why bother with the added complexity?

 

[yungman]

Thanks, I thought I missed something.