Coordinate geometry › Parabolas, ellipses and hyperbolas

Arches

Solve the first problem 4 problems

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1. Water width under a parabolic arch ●●○○○ 20 ptsThe vertex of a parabolic arch bridge is 2 meters above the water surface, and the width of the water surface is 8 meters. When the water level rises by $\frac{1}{2}$ meter, find the width of the water surface in meters. Round to two decimal places.
2. Height of semi-elliptical arch ●●○○○ 20 ptsAn arch is in the form of a semi-ellipse. It is 8 m wide at the base and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end (measured horizontally along the base). Round to two decimal places.
3. Width of a parabolic arch base ●●○○○ 20 ptsA parabolic arch is 18 m high, and its axis is vertical. The width of the arch 8 m below the top is 64 m. Find the width of the arch at its base.

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