| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2008 |
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| Session | November |
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| Topic | Implicit equations and differentiation |
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5 The curve \(C\) has equation
$$x ^ { 2 } - x y - 2 y ^ { 2 } = 4 .$$
Show that, at the point \(A ( 2,0 )\) on \(C , \frac { \mathrm {~d} y } { \mathrm {~d} x } = 2\).
Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(A\).