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

let C_{1}: y = x - 1/2 x^{2}and C_{2}: x = y - 1/2 y^{2}be curves on the xy plane.

1. find the equation of the tangent to the curve C_{1}at x = k

2. suppose the line obtained in 1) is also tangent to the curve C_{2}. find all values of k and the equations of the tangents.

3. evaluate the area of the figure enclosed by all tangents obtained in 2) and the curve C_{2}

2. Relevant equations

derivatives, equation of tangent

3. The attempt at a solution

1. I've done it. I got : y = (1-k) x + 1/2 k^{2}

2.

differentiate C_{2}with respect to x :

1 = dy/dx - y dy/dx

dy/dx = 1/(1-y) = m

so, 1/(1-y) = 1-k

then.....I...gave up...

**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: Tangent of two curves

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