Question

Find the radius of curvature of y^2=a^2(a-x)/x at (0,0)

Answer 1

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Answer 2

Answer:

y²=4a²(2a-x) /x = 4a²(2a/x - 1)

Differentiating implicitly w.r.t. y gives 2y = 4a²(-2a/x²) dx/dy

So y = -(4a³/x²) dx/dy

So dx/dy = -x²y/(4a³)

Differentiating again w.r.t. y gives d²x/dy² = -(x² + 2xy dx/dy)/(4a³)

So, when y=0:

x=2a

dx/dy=0

d²x/dy² = -((2a)² + 0)/(4a³) = -1/a

Then R = √[1 + (dx/dy)²]³/|d²x/dy²| = a

Step-by-step explanation:

hope you got it