| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2019 |
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| Session | November |
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| Topic | Implicit equations and differentiation |
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5 The equation of a curve is \(2 x ^ { 2 } y - x y ^ { 2 } = a ^ { 3 }\), where \(a\) is a positive constant. Show that there is only one point on the curve at which the tangent is parallel to the \(x\)-axis and find the \(y\)-coordinate of this point.