Point on curve closest to point (18,0)

[glasvegas]

Homework Statement

Find the point on the curve y=x^2 that is closest to the point (18,0)

Homework Equations

y=x^2

The Attempt at a Solution

so, dy/dy=2y

Then I tried to use the fact that the product of 2 straight lines that meet at right angles is -1 to come up with a formula for a straight line through (18,0) that meets at a tangent to the closest point of the curve but can't seem to get this to work.

Am i barking up the wrong tree here?

Any help appreciated

 

[hotvette]

dy/dy=2y

Wrong, I think you have a typo. I think the approach you are taking is using the equation of the slope of the curve to come up with the equation of the line that goes though the desired point and is perpendicular to the curve. That's a valid approach. Another approach is to write an expression for distance to the curve from the point and minimize it.

 

[glasvegas]

Oops yeah that was a typo.

I have managed to solve using distance formula.

I'm still curious as to how to do it using the perpendicular to tangent method.

 

[hotvette]

I'm still curious as to how to do it using the perpendicular to tangent method.

1. The slope of the curve is y'

2. The slope of a line normal to the curve is -1/y' (i.e. negative reciprocal)

3. Use the point-slope form of a line to get an expression for the line going through the desired point using the slope from (2).

4. Find the intersection of the curve with the line from (3) by setting the equation of the line equal to the equation for the curve and solving for x.