Question #df419

1 Answer
Nov 27, 2017

The distance is #=4u#

Explanation:

The easiet way is graphically.

Plot the parabola and the point and you will see the shortest distance

graph{(y-16+x^2)((x-4)^2+(y-16)^2-0.2)=0 [-22.2, 29.12, -6.27, 19.4]}

From the graph, you can see that the point #(4,16)# is at the same height as the maximum of the parabola.

The distance is #=4u#

The vertex form of a parabola is

#y=a(x-h)^2+k# where #(h,k)# is the vertex

Here, we have

#y=16-x^2#

#y=-x^2+16#

#y=-(x-0)^2+16#

As #a<0#, the parabola opens downwards and the vertex is at #(0,16)#

If you need, I can calculate the shortest distace with partial derivatives.