The standard form of the equation of an ellipse centered at the origin with vertices (±a, 0) and co-vertices (0, ±b) is:
(x^2/a^2) + (y^2/b^2) = 1
In this case, the vertices are (-6, 0) and (6, 0) and the co-vertices are (0, 4) and (0, -4).
Since the vertices are on the x-axis, a = 6 and since the co-vertices are on the y-axis, b = 4.
Plugging these values into the standard form equation, we get:
(x^2/6^2) + (y^2/4^2) = 1
Simplifying further:
x^2/36 + y^2/16 = 1
Therefore, the equation of the ellipse in standard form is:
x^2/36 + y^2/16 = 1
what is an equation in standard form of an ellipse centered at the origin with vertex (-6, 0) and co-vertex (0,4)?
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