An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2m from the vertex of the parabola? 

Let AB be the parabolic arch having O at the vertex and the vertical line OY as the axis.
The parabola open upwards
∴   Its equation is of the form  ...(i)
     Width of the arch, LM = 5 m
                           OM = 2.5 m
      Height of the arch, BM = 10 m
∴ Co-ordinates of point B are (2.5, 10)
Since point B lies on the parabola 
∴     
∴     From (i), the equation of the parabola is: 
or                                                                                  ...(ii)
We have to find the width PQ of the arch at a distance ON = 2 m from the vertex.
Let                       PQ = d  NQ = 
∴    Co-ordinates of point Q are 
Putting it in (ii), we get 
Hence, the width of the arch = d =  or 2.23 (approx).