Find an equation for the ellipse described
center (0,0); major axis horizontal with length 18; length of minor axis is 4
recall that the ellipse
x^2/a^2 + y^2/b^2
has
major axis 2a
minor axis 2b
To find the equation of an ellipse, we can use the standard form equation:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where (h,k) represents the center coordinates, "a" represents the semi-major axis length, and "b" represents the semi-minor axis length.
Given that the center is (0,0), we substitute h = 0 and k = 0 in the equation:
(x-0)^2/a^2 + (y-0)^2/b^2 = 1
which simplifies to:
x^2/a^2 + y^2/b^2 = 1
The major axis is horizontal with a length of 18, so the semi-major axis length "a" is half of the major axis length, which means a = 18/2 = 9.
The length of the minor axis is 4, so the semi-minor axis length "b" is half of the minor axis length, which means b = 4/2 = 2.
Finally, we substitute the values of "a" and "b" into the equation:
x^2/9^2 + y^2/2^2 = 1
Simplifying further gives us:
x^2/81 + y^2/4 = 1
Therefore, the equation of the ellipse is:
x^2/81 + y^2/4 = 1