Question
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)
Answers
GPT 3.5
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.
[(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.