#### Question

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

#### Solution

Since the height and width of the arc from the centre is 2 m and 8 m respectively, it is clear that the length of the major axis is 8 m, while the length of the semi-minor axis is 2 m.

The origin of the coordinate plane is taken as the centre of the ellipse, while the major axis is taken along the *x*-axis. Hence, the semi-ellipse can be diagrammatically represented as

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Solution An Arch is in the Form of a Semi-ellipse. It is 8 M Wide and 2 M High at the Centre. Find the Height of the Arch at a Point 1.5 M from One End. Concept: Ellipse - Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse.