The standard form equation of an ellipse centered at the origin with the major axis parallel to the y-axis is:
(x^2) / (b^2) + (y^2) / (a^2) = 1
where a is the length of the semi-major axis and b is the length of the semi-minor axis.
The vertex (0,sqrt(29)) is on the major axis, so it corresponds to the point (0,a) in the equation. Therefore,
a = sqrt(29)
The covertex (-5,0) is on the minor axis, so it corresponds to the point (b,0) in the equation. Therefore,
b = 5
Substituting these values into the standard form equation, we get:
(x^2) / (5^2) + (y^2) / (sqrt(29)^2) = 1
Simplifying:
x^2 / 25 + y^2 / 29 = 1
This is the equation of the ellipse centered at the origin, with semi-major axis sqrt(29) and semi-minor axis 5.
Write an equation of an ellipse centered at the origin, satisfying the given conditions. vertex (0,sqrt (29)); covertex (-5,0)
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