Question

Write an equation in standard form of the ellipse that is 16 units high and 10 units wide. The center of theellipse is (0,0).+31= 1

Answer 1

x²/25 +y²/64 = 1

Explanation:

You want the standard form equation of an ellipse 16 units high and 10 units wide, centered at the origin.

Ellipse

The standard-form equation of an ellipse centered at the origin is ...

x²/a² +y²/b² = 1

where 'a' and 'b' are the lengths of the semi-axes in the x- and y-directions, respectively.

Application

If the ellipse is 10 units wide, its axis in the x-direction is 10, so half that length is a = 10/2 = 5.

If the ellipse is 16 units high, its axis in the y-direction is 16, so half that length is b = 16/2 = 8.

The equation is ...

x²/5² +y²/8² = 1

x²/25 +y²/64 = 1

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