Find Min Distance b/w Parabolas: 7/(4*root2)

[erisedk]

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.

 

[Dick]

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.

 

[erisedk]

Ohhh ok. I didn't realize 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