Answer:
(x +4)²/25 +(y -3)²/16 = 1
Explanation:
You want the equation of the ellipse with center (-4, 3) and semi-axes 5 and 4 in the x- and y-directions, respectively.
Ellipse equation
The standard form equation for an ellipse with center (h, k) and sem-axes 'a' and 'b' in the x- and y-directions, respectively, is ...
(x -h)²/a² +(y -k)²/b² = 1
Using the given values, we find the equation to be ...
(x +4)²/25 +(y -3)²/16 = 1
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Additional comment
The longer of the two axes is the "major" axis, and its end points are the "vertices". For the purpose of an ellipse with center, vertices, and co-vertices specified, the equation is not affected by which axis is longer.
Effectively, this is the equation of a circle with different scale factors in the x- and y-directions.
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