Moderate -0.3 This is a straightforward parametric-to-Cartesian conversion requiring algebraic manipulation: rearranging x = 1/(1+t) to find t in terms of x (giving t = 1/x - 1), then substituting into the y equation and simplifying. While it involves rational expressions requiring careful algebra, it's a standard textbook exercise with no conceptual difficulty or novel insight required, making it slightly easier than average.
2 A curve is defined parametrically by the equations
$$x = \frac { 1 } { 1 + t } , \quad y = \frac { 1 - t } { 1 + 2 t }$$
Find \(t\) in terms of \(x\). Hence find the cartesian equation of the curve, giving your answer as simply as possible.
2 A curve is defined parametrically by the equations
$$x = \frac { 1 } { 1 + t } , \quad y = \frac { 1 - t } { 1 + 2 t }$$
Find $t$ in terms of $x$. Hence find the cartesian equation of the curve, giving your answer as simply as possible.
\hfill \mbox{\textit{OCR MEI C4 2011 Q2 [5]}}