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An arc is in the form of a semi-ellipse....

An arc is in the form of a semi-ellipse. It is `8m` wide and `2m` high at the centre. Find the height of the arch at a point `1. 5c m` from one end.

Text Solution

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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,
The equation of the semi-ellipse will be of the form `(x^2)/(a^2)+(y^2)/(b^2)=1,y>=0,`
where `a` is the semi major axis
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