| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2008 |
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| Session | June |
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| Topic | Implicit equations and differentiation |
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6 The equation of a curve is \(x y ( x + y ) = 2 a ^ { 3 }\), 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.