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## Homework Statement

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}

## Homework Equations

derivatives, equation of tangent

## 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...