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Home NJC Parametric Equations Tutorial Q5 A curve $C$ is given by the parametric equations $x={{t}^{2}}+3$, $y=tleft( {{t}^{2}}+3 right)$. (i) Find a Cartesian equation of $C$ and hence show, using
These Ten-Year-Series (TYS) worked solutions with video explanations for 2013 A Level H2 Mathematics Paper 1 Question 11 are suggested by Mr Gan. For any comments or suggestions please contact
2021 ACJC Promo Q8 The figure below shows a cross-section $OBCE$ of a car headlight whose reflective surface is modelled in suitable units by the curve with parametric equations $x=aleft(
2020 SAJC Promo Q9 A curve $C$ has parametric equations $x=ln (sec theta )$,$y=ln (sin theta )$, $0<theta <frac{pi }{2}$. (i) Sketch the curve $C$, stating the equation of any
2020 TMJC Promo Q9 A curve $C$ has parametric equations $x=cos 2theta $ and $y=cos text{ec }theta $, where $0<theta le frac{pi }{2}$. (i) Show that $frac{text{d}y}{text{d}x}=frac{1}{4}cos text{e}{{text{c}}^{3}}theta $. What
2020 NJC P2 Q4 The curve ${{C}_{1}}$ has parametric equations $x=4+4sin theta $, $y=2cos theta $, where $-frac{pi }{2}le theta le frac{pi }{2}$. Sketch ${{C}_{1}}$, labelling any points where ${{C}_{1}}$
2020 ACJC P1 Q7 A hot air balloon company gives a sticker to each passenger who is going for a ride. The sticker is in the shape of a curve
2020 TMJC P2 Q2 A curve $C$ has parametric equations $x=1+{{text{e}}^{t}}$, $y=t-{{text{e}}^{t}}$ for $t>0$. (i) Sketch the graph of $C$. [2] (ii) Find the equation of the tangent to $C$
2021 NYJC P1 Q8 A curve $C$ has parametric equations $x=a{{sin }^{5}}t$, $y=a{{cos }^{5}}t$ where $a$ is a positive constant. The tangent to $C$ at a general point with parameter
2021 MI P1 Q8 A curve $C$ has parametric equations $x=cot t+2$, $y=sec t$, $-frac{pi }{2}<t<0$ (i) Sketch the graph of $C$, indicating the equations of any asymptotes. [2] (ii)