| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2016 |
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| Session | November |
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| Topic | Implicit equations and differentiation |
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4 The equation of a curve is \(x y ( x - 6 y ) = 9 a ^ { 3 }\), where \(a\) is a non-zero constant. Show that there is only one point on the curve at which the tangent is parallel to the \(x\)-axis, and find the coordinates of this point.