(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the shortest distance between,

[tex]y = x^{2} - 8x + 15[/tex] and,

[tex]2y + 7 + 2x^{2} = 0[/tex]

2. Relevant equations

3. The attempt at a solution

Rearranging the 2nd function into a function of y in terms of x,

[tex] y = -x^{2} - \frac{7}{2}[/tex]

From here I was able to graph the two in the x-y plane. (See figure)

Now the shortest distance between them will be a vector that runs from one curve to the other, and is perpendicular to both curves, correct?

How can I go about finding this vector? If I can somehow create this vector, I can compute his magnitude and I'll have the shortest distance between the two curves.

Any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Shortest distance between 2 curves

**Physics Forums | Science Articles, Homework Help, Discussion**