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Distance on a Parabola

  1. Apr 7, 2009 #1
    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.
     
  2. jcsd
  3. Apr 7, 2009 #2
    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)
     
  4. Apr 7, 2009 #3
    I'm kind of confused on step 2. How do you find the tangent?
     
  5. Apr 7, 2009 #4
    you know the x point so find its derivative and use the point slope formula and solve for x
     
  6. Apr 8, 2009 #5
    I still don't really understand. Do you think you can show it?
     
  7. Apr 8, 2009 #6
    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?
     
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