# How do you find the points on the parabola #2x = y^2# that are closest to the point (3,0)?

##### 2 Answers

Points are (2.2) and (2, -2)

Let there be any point (x,y) on this parabola. The distance 's' of this point from point (3,0) is given by

Differentiating the equation

It is thus 3-x=1, x=2, and then y=2, -2. The nearest points are (2,2) and (2,-2)

An alternative starts the same as bp's solution:

Let

Note that, since

Our job now is to minimize the function:

(It should be clear that we can minimize the distance by minimizing the square of the distance.)

To minimize, differentiate, find and test critical numbers.

The question asks for points on the graph, so we finish by finding points on the graph at which

The points are: