Restricting Domain and Range in broken conics

[xxfamousxx91]

Homework Statement

How do you know whether you restrict the domain or range with a horizontal ellipse ?

Homework Equations

x^2/49 +y^2/10=1

The Attempt at a Solution

 

[HallsofIvy]

Since y² is never negative, x will be largest when y= 0. And when y= 0, $x^2/49= 1$, $x^2= 49$, $x= \pm 7$. $-7\le x\le 7$. Similarly, if x= 0 $y^2/10= 1$ so $y= \pm\sqrt{10}$. If x is not zero, $y^2$ is smaller than 10 so $-\sqrt{10}\le y\le\sqrt{10}$.