A curve $C$ is given by the parametric equations $x={{t}^{2}}+3$, $y=t\left( {{t}^{2}}+3 \right)$. F

Question

A curve $C$ is given by the parametric equations $x={{t}^{2}}+3$, $y=t\left( {{t}^{2}}+3 \right)$. Find a Cartesian equation of $C$ and hence show, using an algebraic method, that the curve is symmetrical about the $x$-axis. Show, using an algebraic method, that there is no part of the curve for which $x Sketch $C$, indicating clearly the points where the curve crosses the $x$- and $y$- axes, if any.

Accepted Answer

$y^2 = x^3 - 3x^2$

NJC Parametric Equations Tutorial Q5

NJC Parametric Equations Tutorial Q5

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