Question

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)?

Answer 1

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.