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.