Write an equation in standard form of an ellipse that is 8 units high and 18 units wide. The center of the ellipse is (0, 0)
The general form of the equation of an ellipse with center (h, k) is given by:
[(x-h)^2 / a^2] + [(y-k)^2 / b^2] = 1,
where a is the length of the semi-major axis and b is the length of the semi-minor axis.
In this case, since the center of the ellipse is (0, 0) and the ellipse is 8 units high and 18 units wide, we have a = 9 (half of the width) and b = 4 (half of the height).
Therefore, the equation of the ellipse in standard form is:
[(x-0)^2 / 9^2] + [(y-0)^2 / 4^2] = 1.
Simplifying, the equation becomes:
[x^2 / 81] + [y^2 / 16] = 1.