Question 1117685: I need help with this: https://imgur.com/F0nowam
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the domain is all possible values of x that lead to one or more real values of y.
that would be -2 <= x <= 2.
the range is all real values of y that are the result of the equation working on all real values of x.
that would be -3 <= y <= 3
the y-intercepts are the value of y when the value of x is equal to 0.
those points would be (0,-3) and (0,3).
the x-intercepts are the value of x when the value of y is equal to 0.
those point would be (-2,0) and (2,0).
the center of the ellipse is at (0,0).
that point is in the middle of the ellipse.
unlike a circle, the distance to every point on the ellipse is not the same.
however, the center of the ellipse is at the center of any line drawn through it that is intersecting with the perimeter of the ellipse.
the two lines intersecting with the perimeter of the ellipse shown are the major axis and the minor axis.
the major axis is the vertical line that extends from (0,-3) to (0,3) and the center lies halfway between those points at (0,0).
the minor axis is the horizontal line that extends from (0,-2) and (0,2) and the center lies halfway between those points at (0,0).
you can take any line that cuts through the center and intersects with the perimeter of the ellipse, and the center will be the midpoint of that line.
here's a reference on ellipses that you might find informative.
https://www.mathsisfun.com/geometry/ellipse.html
here's a reference on domain and range you might find informative.
https://www.intmath.com/functions-and-graphs/2a-domain-and-range.php
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