SOLUTION: what is the ellipse equation for a ellipse with the center (1,-3) major axis parallel to y with length 10 minor axis 4

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Question 822091: what is the ellipse equation for a ellipse with the center (1,-3) major axis parallel to y with length 10 minor axis 4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  • "major axis parallel to [the] y [axis]" tells us that this ellipse is vertically oriented. So we will be using the standard form for the equation of such an ellipse:
    %28x-h%29%5E2%2Fb%5E2+%2B+%28y-k%29%5E2%2Fa%5E2+=+1
    where h and k are the coordinates of the center, a is the distance from the center to a vertex on the major axis and b is the distance from the center to a vertex on the minor axis.
  • We have been given the center, (1, -3), so h = 1 and k = -3.
  • We have been given that the length of major axis is 10. Since this length is from vertex to vertex and since the center is the midpoint of the major axis, the distance from the center to a vertex is half the length. So a = half of 10 or 5.
  • We have been given that the length of minor axis is 4. Since this length is from vertex to vertex and since the center is the midpoint of the minor axis, the distance from the center to a vertex is half the length. So b = half of 4 or 2.
Putting this all together we get:
%28x-%281%29%29%5E2%2F%282%29%5E2+%2B+%28y-%28-3%29%29%5E2%2F%285%29%5E2+=+1
which simplifies to:
%28x-1%29%5E2%2F4+%2B+%28y%2B3%29%5E2%2F25+=+1