Minimum distance

  • Thread starter erisedk
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  • #1
374
7
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Homework Statement


Find the minimum distance between the curves y^2 - xy - 2x^2 = 0 and y^2 = x - 2.
Ans: 7/(4*root2)

Homework Equations




The Attempt at a Solution


It's supposed to be done using concepts from parabolas. I tried using calc but it got convoluted.
 

Answers and Replies

  • #2
Dick
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Homework Statement


Find the minimum distance between the curves y^2 - xy - 2x^2 = 0 and y^2 = x - 2.
Ans: 7/(4*root2)

Homework Equations




The Attempt at a Solution


It's supposed to be done using concepts from parabolas. I tried using calc but it got convoluted.

y^2 - xy - 2x^2 splits into two linear factors. That makes it easier since the graph becomes two lines.
 
  • #3
374
7
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
 

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