How to Find the Equation of the Normal for a Curve | IB Math Explained

Stop scrolling — this curve may look scary at first, but the normal line comes out super clean! In this step-by-step tutorial, we’ll solve for the equation of the normal at the point (3, 3) for the curve defined by:

x³ + y³ = 6xy

We'll walk through the process of differentiating the equation implicitly and solving for the gradient of the normal. With clear explanations, we’ll also show you how to use the point-slope form to get the final equation of the normal line.

Steps Covered in This Video:

Implicit differentiation of the equation x³ + y³ = 6xy

How to isolate and solve for dy/dx (derivative)

Calculating the gradient of the tangent line at the point (3, 3)

Finding the gradient of the normal line using the negative reciprocal

Writing the equation of the normal line in point-slope form

This video is perfect for students tackling IB Math and anyone looking for a quick explanation on finding the equation of a normal line to a curve!

🔑 Key Terms: Implicit Differentiation, IB Math, Equation of the Normal, Point-Slope Form, Derivatives, Gradient of Tangent, Curve Equation, Mathematics Tutorial.

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