A curve $C$ has parametric equations $x=2\sin t$ and $y=3\cos t$ where $0\le t\le 2\pi $. Find the e

Question

A curve $C$ has parametric equations $x=2\sin t$ and $y=3\cos t$ where $0\le t\le 2\pi $. Find the equations of the tangent and normal to the curve at the point $P$ where $t=\frac{\pi }{4}$. The tangent and normal to the curve at point $P$ meet the $x$-axis at points $Q$ and $R$ respectively. Show that the exact area of triangle $PQR$ is $\frac{39}{8}$ units$^{2}$. [7] Find the Cartesian equation of $C$ and sketch $C$. [3]

Accepted Answer

(i) Tangent: $y = -\dfrac{3}{2}x + 3\sqrt{2}$, Normal: $y = \dfrac{2}{3}x + \dfrac{5\sqrt{2}}{6}$ (ii) $\dfrac{x^2}{4} + \dfrac{y^2}{9} = 1$

2011 CJC P2 Q1

2011 CJC P2 Q1

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