Find the equation of the normal at the point `(a m^2,a m^3)`for the cu

1.	Find the equation of the normal at the point `(a m^2,a m^3)`for the curve `a y^2=x^3`.
Answer» Equation of curve ` ay^(2) = x^(3)` ` rArr 2ay (dy)/(dx) = 3x^(2)` ` rArr (dy)/(dx) = (3x^(2))/(2ay)` Slope of tangent at point `(am^(2), am^(3)) = (3(am^(2)^(2))/(2a(am^(3))) = (3m)/2` ` rArr" Slope of normal "=(-2)/(3m)` and equation of normal ` y-am^(3) = - 2/(3m) (x- am^(2))` ` rArr 3my - 3am^(4) = - 2x + 2am^(2)` ` rArr 2x + 3my - 3am^(4) - 2am^(2) = 0`

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

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