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

 

[Architeuthis Dux]

Restricting the domain and range in broken conics, such as a horizontal ellipse, is important in order to accurately represent the data and avoid any misleading information. In the equation x^2/49 +y^2/10=1, the domain and range can be restricted by setting limits on the values of x and y. For a horizontal ellipse, the domain can be restricted by setting a limit on the values of x, since the major axis of the ellipse is parallel to the x-axis. This can be done by determining the x-intercepts of the ellipse and setting those as the limits for the domain. Similarly, the range can be restricted by setting limits on the values of y, since the minor axis of the ellipse is parallel to the y-axis. This can be done by determining the y-intercepts of the ellipse and setting those as the limits for the range. It is important to carefully consider the data and the purpose of the graph when determining the appropriate restrictions for the domain and range in broken conics.