# Could i Have help with a problem i am stuck on please.

• December 10th 2009, 12:06 PM
Could i Have help with a problem i am stuck on please.
Hello, I have a small problem that i am having trouble with,

Find the co-ordinates of the point on the curve y=sqrt(x) which is closest to the point (5/2,0)

I already know a little about the process, I know the formula to find distance from the origin is sqrt(x^2+y^2) and I substitute sqrt(x) for y,
But then I simplify it down and get sqrt(-4x).
If i could have some pointers i would be really greatfull.
Thank you.
• December 10th 2009, 12:22 PM
TheEmptySet
Quote:

Hello, I have a small problem that i am having trouble with,

Find the co-ordinates of the point on the curve y=sqrt(x) which is closest to the point (5/2,0)

I already know a little about the process, I know the formula to find distance from the origin is sqrt(x^2+y^2) and I substitute sqrt(x) for y,
But then I simplify it down and get sqrt(-4x).
If i could have some pointers i would be really greatfull.
Thank you.

This distance between two points is given by

$d=\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}$

So the distance between the point and the function is

$d=\sqrt{\left(\frac{5}{2}-x \right)^2+(0-\sqrt{x})^2}$

Note that minimizing the square of the distance will also solve the problem

I hope this helps