1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Minimum distance

  1. Oct 26, 2014 #1
    • No effort shown
    1. The problem statement, all variables and given/known data
    Find the minimum distance between the curves y^2 - xy - 2x^2 = 0 and y^2 = x - 2.
    Ans: 7/(4*root2)

    2. Relevant equations

    3. The attempt at a solution
    It's supposed to be done using concepts from parabolas. I tried using calc but it got convoluted.
  2. jcsd
  3. Oct 26, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    y^2 - xy - 2x^2 splits into two linear factors. That makes it easier since the graph becomes two lines.
  4. Oct 27, 2014 #3
    Ohhh ok. I didn't realise that was a pair of straight lines.
    I did it now. Split it into y=-x and y=2x. Drew a rough graph. It's clear from the graph that y=-x is closer. So, using the slope form of tangent to a parabola, I wrote the equation of tangent with the slope -1, and figured out the distance between the two parallel lines, which comes out to be the answer. Thanks :D
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted