A curve $C$ has parametric equations \[x = \operatorname{cosec} \theta + 2, \quad y = 3 \cot \thet

Question

A curve $C$ has parametric equations $$x = \operatorname{cosec} \theta + 2, \quad y = 3 \cot \theta, \quad \text{where}\hspace{0.5em} 0 < \theta < \pi.$$ Find a cartesian equation of $C$.[2] Sketch $C$, indicating all the necessary features, including the equations of any asymptotes.[3]

Accepted Answer

(a) $(x-2)^2-\left(\dfrac y3\right)^2=1$ (b) right branch only, centre $(2,0)$, vertex $(3,0)$, asymptotes $y=\pm3(x-2)$

Graphing Techniques - Graphs of Conic Sections

Graphing Techniques - Graphs of Conic Sections

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