Level 3 Differentiation Walkthrough

Question 2(e)

2022 Paper - Tangent line and distance between intercepts

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Question

The curve with equation \((y-5)^2=16(x-2)\) has a tangent of gradient \(1\) at point \(P\).

This tangent intersects the \(x\)- and \(y\)-axes at points \(R\) and \(S\) respectively.

\[ \text{Prove that the length } RS \text{ is } 7\sqrt{2}. \]

You must use calculus and show any derivatives that you need when solving this problem.

Both implicit differentiation and rearranging to the upper branch \(y=5+4\sqrt{x-2}\) are valid methods here.

Try the question yourself first. If you get stuck, open the hints before using the full walkthrough.