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

Show that the gradient of the curve [tex]\frac{a}{x}+\frac{b}{y}=1[/tex] is [tex]-\frac{ay^2}{bx^2}[/tex]. The point (p,q) lies on both the straight line [itex]ax+by=1[/tex] and [tex]\frac{a}{x}+\frac{b}{y}=1[/tex] where ab =/= 0. Given that, at this point, the line and the curve have the same gradient, show that p=±q.

3. The attempt at a solution

[tex]\frac{a}{x}+\frac{b}{y}=1[/tex]

[tex]\frac{dy}{dx}=-ax^{-2}-by^{-2}[/tex]

[tex]-\frac{b}{y^2}\frac{dy}{dx}=\frac{a}{x^2}[/tex]

[tex]\frac{dy}{dx}=-\frac{ay^2}{bx^2}[/tex]

1. The problem statement, all variables and given/known data

Not sure how to calculate the next part..

2. Relevant equations

3. The attempt at a solution

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

Join Physics Forums Today!

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

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

# Homework Help: Show that the gradient of the curve

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