Question
Write the equation of an ellipse centered at the origin with height 8 units and width 16 units. Be sure to show or explain how you got your answer
Answers
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The standard equation for an ellipse centered at the origin is:
(x^2/a^2) + (y^2/b^2) = 1
where "a" is the semi-major axis (half the width) and "b" is the semi-minor axis (half the height).
In this case, the height is 8 units and the width is 16 units, so:
a = 16/2 = 8
b = 8/2 = 4
Substituting these values into the standard equation gives:
(x^2/8^2) + (y^2/4^2) = 1
Simplifying, we get:
(x^2/64) + (y^2/16) = 1
Therefore, the equation of the ellipse centered at the origin with height 8 units and width 16 units is:
(x^2/64) + (y^2/16) = 1
(x^2/a^2) + (y^2/b^2) = 1
where "a" is the semi-major axis (half the width) and "b" is the semi-minor axis (half the height).
In this case, the height is 8 units and the width is 16 units, so:
a = 16/2 = 8
b = 8/2 = 4
Substituting these values into the standard equation gives:
(x^2/8^2) + (y^2/4^2) = 1
Simplifying, we get:
(x^2/64) + (y^2/16) = 1
Therefore, the equation of the ellipse centered at the origin with height 8 units and width 16 units is:
(x^2/64) + (y^2/16) = 1