Chain Rule & Integration by Substitution
Review question

Can we show this parabola and this ellipse meet at right angles?
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Ref: R7042
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Question

The normal at a point \(P\) on the parabola \(y^2=4ax\) meets the ellipse \(2x^2+y^2=c^2\) in the points \(M\), \(N\). Prove that \(P\) is the mid-point of \(MN\).

Hence, or otherwise, prove that the conics cut at right angles.

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UCLES A level Mathematics Scholarship paper, QP 184, 1952, Q5

Question reproduced by kind permission of Cambridge Assessment Group Archives. The question remains Copyright University of Cambridge Local Examinations Syndicate (“UCLES”), All rights reserved.

 Last updated 06-Sep-16
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