Find the equation of normal to the curve at the point whose x coordinate is

given: ay² = x³ is the curve, and the point is am² at which normal is required

Differentiating the curve to get the slope of the tangent

Formula: m_tangentm_normal = - 1

Finding the corresponding y coordinate for the given x coordinate

ay² = a³m⁶

y² = a²m⁶

y = am³ or - am³

therefore

Now, we know that,

Equation of line: (y – y₁) = m_normal(x – x₁)

the equation of normal is

or