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Question from jessica, a student:

An arch in the form of a semi ellipse has a span of 10 meters and a central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis.

Hi Jessica,

Assume the ellipse is in standard position with its centre at the origin, the major axis along the x-axis and its minor axis along the y-axis.

ellipse

The equation of the ellipse is then

equation

Since (5, 0) and (0, 4) are on the ellipse if you substitute these values into the equation you can solve for a and b. Then substitute x = 3 into the equation and solve for y.

Penny

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