Find the equation of the normal to the curve `a y^2=x^3` at the point `(a m^2,\ a m^3)` .

Explanation

`a y^{2}=x^{3}`

Differentiating both sides w.r.t.x ,


`2 a y frac{d y}{d x}=3 x^{2} `

`Rightarrow frac{d y}{d x}=frac{3 x^{2}}{2 a y}`

Slope of tangent `=(frac{d y}{d x})_{(a m^{2}, a m^{3})}=frac{3 a^{2} m^{4}}{2 a^{2} m^{3}}=frac{3 m}{2}`

Given `(x_{1}, y_{1})=(a m^{2}, a m^{3})`

Equation of normal is,

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