# Restricting Domain and Range in broken conics

1. Mar 22, 2009

### xxfamousxx91

1. The problem statement, all variables and given/known data
How do you know whether you restrict the domain or range with a horizontal ellipse ?

2. Relevant equations
x^2/49 +y^2/10=1

3. The attempt at a solution

2. Mar 22, 2009

### HallsofIvy

Staff Emeritus
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 $-\sqrt{10}\le y\le\sqrt{10}$.