Question

The feet of a commemorative parabolic steel arch 100m high are 200m apart. Determine whether the focus of the arch is above or below ground and indicate the number of feet it lies above or below ground.
75 ft above

25 ft above

25 ft below

75 ft below

Answer 1

The focus of the arch is 75 ft. above ground

Answer 2

First of all, there should be coherence for the units of measurement -- either they are all meters or they are all ft. I would assume they are all ft. The correct answer is 75 ft above. T The explanation is the following: suppose the ground level is the x-axis, the 2 feet of the arch lie respectively on (0,0) and (100,0) on the ground level. Since the arch is 100ft high, the vertex of the parabola will be the point (100,100). Thus, we can find the equation describing the parabola by putting the three points we know in a system and we find that the equation of the parabola is y=(-1/100)x^2+2 To find the focus F, we apply the formula for the focus of a vertical axis parabola, i.e. F(-b/2a;(1-b^2+4ac)/4a). By substituting a=-1/100, b=2 and c=0 into the formula, we find that the coordinates of the focus F are (100,75). So we conclude that the focus lies 75ft above ground.