Conic Sections

Geometry Level 2

An arch is in the form of a semi-ellipse. It is 8 meters wide and 2 meters high at the centre. Find the height of the Arch at a point 1.5 meters from one end. Answer up to 2 decimal places in meters. (Take sq.root 39=6.24)

The answer is 1.56.

1 solution

Tom Engelsman
Mar 27, 2021

The elliptical arch (which has major semi-axis = $4$ and minor semi-axis = $2$ ) can be modeled per the equation:

$\frac{x^2}{16} + \frac{y^2}{4} = 1$

Taking a point that is $1.5$ units away from either end of the arch ( $x = \pm 2.5$ ), the corresponding vertical height computes to:

$y = 2 \cdot \sqrt{1 - (2.5^{2})/16} \approx \boxed{1.56}.$

Conic Sections

The answer is 1.56.

1 solution

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