How do you write an equation of an ellipse given the major axis is 20 units long and parallel to the y-axis and the minor axis is 6 units long, center at (4,2)?

1 Answer
Douglas K.
Jan 27, 2017

The Cartesian form of the equation of an ellipse with a vertical major axis is (y-k)^2/a^2+(x-h)^2/b^2=1" [1]"
where (h,k) is the center, 2a is the major axis, and 2b is the minor axis.

Explanation:

Given that the center is (4,2), substitute 4 for h and 2 for k into equation [1]:

(y-2)^2/a^2+(x-4)^2/b^2=1" [2]"

Given that the major axis is 20 units, substitute 10 for "a" into equation [2]:

(y-2)^2/10^2+(x-4)^2/b^2=1" [3]"

Given that the minor axis is 6 units, substitute 3 for "b" into equation [3]:

(y-2)^2/10^2+(x-4)^2/b^2=1" [4]"

Equation [4] is specified equation. The following graphs is ellipse with the center and the end points of the major and minor axes plotted.
![Desmos.com](useruploads.socratic.org)

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