Each point on the line can be expressed as a coordinate in the form...
Why? A coordinate is of the form and
So what to do is think in terms of Pythagoras triangle... You have two sides, one of length , one of length and one unknown side that you must find.
Why? Well just think of the coordinate as being distance along the x-axis then distance up to get to the point. This will form a right angled triangle with side lengths and
So, let's call this unknown side , using the standard Pythagoras formula we get...
Now you finish this off by expanding everything and you will be left with a formula of the form...
then just take square roots to get,
which will be your answer.
This will happen at one of two places.
A critical point,
An end point of the range of . (i.e. ).
Immediately you can see that that if then (if not I'll explain).
So that leaves you to find critical points...
I'll start you off...
Solve for this to be 0 and what does that tell you..?