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Write the equation of the ellipse graphed below.

Write the equation of the ellipse graphed below.-example-1
User Ostn
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1 Answer

4 votes

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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User David Ranieri
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