Shortest Distance on a Parabola: Point to Point Calculation

[karisrou]

2. Find the shortest distance from the point (1,4) to a point on the parabola y^2 = 2x

Not really sure what to do here next. I'd imagine i might have to fuse implicit differentiation? But not really sure.

 

[tnutty]

1) solve for x
2) find tangent to curve at x
3) use point slope formula
4) solve for x

your ans should be sqrt(5)

 

[karisrou]

I'm kind of confused on step 2. How do you find the tangent?

 

[tnutty]

you know the x point so find its derivative and use the point slope formula and solve for x

 

[karisrou]

I still don't really understand. Do you think you can show it?

 

[Dunkle]

There are multiple ways to solve this problem. One way is to think about this as an minimization problem. Hint: Let (x,y) be the point on the parabola closest to (1,4) and write out the formula for the distance between these two points. Next, use the relationship between x and y to write the formula in terms of one variable. Now what do you think you should do?