- #1
Uranium235
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Homework Statement
Well I would like to prove that any equation that follows the pattern y=rx-r^(-1) is tangent to some sideways parabola (I know this to be true). Problem is that I need help in finding the parabola in question and actually proving my conjecture. I do know, after graphing, that the parabola has a vertex a (0,0).
Homework Equations
y=rx-r^(-1) any linear system of this form should be tangent to a sideways parabola
y=(ax)^1/2 the equation of a sideways parabola
The Attempt at a Solution
After graphing, I realized that any equation of the form y=rx-r^(-1) where r is positive seems to be always tangent the curve y=-(-4x)^(1/2) while any equation of the form y=rx-r^(-1) where r is negative seems to be always tangent to y=(-4x)^(1/2). I got those values from trial and error only and there is no proof to support it.
Any help in clearing this up will be appreciated since my assignment is due on friday. Thank you!