Find evolute of xy=c^2
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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}}
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}}
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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
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
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