- #1
Delber
- 19
- 0
Homework Statement
For a any parabola with the equation [tex]y=kx^{2}[/tex]
I'm trying to find a curve that intersect every point of the parabola at right angles.
Homework Equations
For a perpendicular intersection the slope is [tex]-\frac{1}{m}[/tex]
The Attempt at a Solution
I took the derivative and then took the negative reciprocal of the derivative.
[tex]\frac{dy}{dx} = -\frac{1}{2kx}[/tex]
Then I isolated the variables on different sides and then integrated. I ended up with:
[tex]y+ \frac{1}{2k}*ln(|x|) = 0 [/tex]
My problem is when I graph the two functions there is only one intersection and I was wondering if there was any flaws in my logic I used to reach my answer.