Question

Find evolute of xy=c^2

Answer 1

The question requires you to find the parametric equations of the evolute of the curve xy=c^2 .
For some reason I keep getting wrong answer.
I use parametric form, x=ct, y=c/t , and so x'=c, y'=-c/t^2, x''=0, y''=2c/t^3 .
Using formula \displaystyle \rho =\frac{\frac{c^3}{t^3}(t^4+1)^{3/2}}{\frac{2c^2}{t^3}}

Answer 2

xy = c^2 is rectangular hyperbola having x and y axis as asymptotes

Here c is constant

it's shape is convex upward

Use parametric coordinates to evaluate

x = ct y = c/t

xy = c^2

x y' + y = 0

y' = -y/x

it's slope of tangent