Find the point on the parabola y=x² nearest to the point (-3,0)?
2 Answers
Explanation:
The distance from any point
For points on
and
more specifically for the point
The problem is to minimize
or equivalently (but slightly simpler) to minimize
The minimum occurs when
That is when
An obvious (by inspection) root is
(and in fact there are no other real roots)
If
then
Explanation:
The squared distance from
We want the minimum
That's a cubic but an easy one. By the time honored method of trying small numbers, we find
The quadratic has no real roots, so