why is the answer x²=160y and not x²=80y?

Question

A parabolic cable hangs between two vertical supports which are 80 m apart. And the depth at the centre of each support is vertically 10m from the supporting level.Taking the lowest point at the point (0, 0), determine the equation of the cable.

this are my workings.. what is wrong?

x²=4py
4p=40²÷20
=80
therefore,
x²=80y

thank you Q.. i think you must be right.. but there is something that i do not understand.. can you or anyone explain to me? the qns says the depth at the centre of each support is vertically 10m from the supporting level. since it is centre, the height of the whole support is 20m.. which is pt (40,20) & (-40, 20).. why cant i use these two pts?

Answer 1

In your second step, you divided by 20, but you should really only divide by 10.

What the problem gives you is that the vertex is (0,0) and two points on the parabola are (40,10) and (-40,10). Therefore, 40^2 = 4p*10, and 4p = 1600/10 = 160, which means the equation is x^2 = 160y.

Hope that helps explain it :)

Answer 2

Picture the following: a suspension bridge.

Your vertical supports are the towers, which are the same height above the water (the vertex, if you will), but are separated by a horizontal distance (the 80m figure).

Your 'support points' are the same vertical distance from the vertex, therefore, you only need to include the height (10m) once.