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Chain Rule & Integration by Substitution

Review question

Can we show that these normals meet on the $x$-axis?
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Ref: R5696

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Question

A curve is given parametrically by the equations \[x=4-t^2,\ y=4t.\]

Find the equations of the normals to the curve at the points where the curve meets the \(y\)-axis. Show that these normals meet on the \(x\)-axis.