# A normal tangent

Calculus Level 4

If the tangent at the point $$(4m^2 , 8m^3 )$$, where $$m > 0$$ is a parameter, to the curve $$\displaystyle x^3 = y^2$$ is normal to it again at some point, then the value of $$m$$ can be expressed as $$\displaystyle \frac{\sqrt{a}}{b}$$, where $$a$$ is square-free.

Enter the value of $$a+b$$.

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