Restricting Domain and Range in broken conics

AI Thread Summary
To determine the restrictions on the domain and range of a horizontal ellipse, the equation x^2/49 + y^2/10 = 1 is analyzed. The maximum x-values occur when y is zero, resulting in the domain restriction of -7 ≤ x ≤ 7. For the range, when x is zero, y can take values from -√10 to √10, leading to the range restriction of -√10 ≤ y ≤ √10. Thus, the domain is restricted by the x-values at the ellipse's horizontal intercepts, while the range is limited by the vertical intercepts. Understanding these restrictions is crucial for graphing and analyzing the ellipse accurately.
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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

 
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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}.
 

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