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Find a Cartesian equation for an ellipse given its center and lengths of its axes

Find a Cartesian equation in standard form for the ellipse with center at (-3,4), semi-axes of lengths 4 and 3, and major axis parallel to the y-axis.


Since the major axis has length 4 and is parallel to the y-axis we have a = 4, and since the minor axis has length 3 we have b = 3. Since the center is at (-3,4) we then have the Cartesian equation

    \[ \frac{(x+3)^2}{9} + \frac{(y-4)^2}{16} = 1. \]

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