Graphing Techniques

2021 HCI P2 Q2 Clear workings and explanations are required for this question. (a) An ellipse of equation $frac{{{x}^{2}}}{{{a}^{2}}}+frac{{{y}^{2}}}{{{b}^{2}}}=1$, where $0<b<a$, has two points called foci ${{F}_{1}}left( -c,0 right)$ and

2021 DHS P1 Q3 The curve $C$ has equation $y=frac{{{x}^{2}}+px+3}{x+q}$, where $p$ and $q$ are non-zero constants and $xne -q$. It is given that the asymptotes of $C$ are $y=x+3$

2018 DHS Promo Q4 The curve $C$ has equation $y=frac{{{x}^{2}}+2x+q}{x-p}$, $xne p$, where $p$ and $q$ are constants. It is given that the line $y=x+3$ is an asymptote of $C$.

2018 MJC Promo Q3 The curve $C$ has equation $y=frac{{{x}^{2}}+ax+10}{x-b}$. The asymptotes of $C$ are $x=3$ and $y=x-2$. (i) Find the values of $a$ and $b$. [2] (ii) Sketch $C$,

SAJC Graphing Techniques Tutorial Q1 The curve $C$ has equation $y=frac{2x-a}{2{{x}^{2}}-b}$, where $a$ and $b$ are positive integers.  $C$ passes through point $left( frac{9}{2},0 right)$ and the equation of an

2015 NJC P1 Q7 (a) It is given that the curve $C$ has equation $y=frac{(x-1)(x-2)}{x-3},text{ }xin mathbb{R},text{ }xne 3.$ Use an algebraic method to find exactly the set of values

2013 VJC P2 Q2  The curve $C$ has equation $y=frac{a{{x}^{2}}+bx+c}{x-1}$, where $a$, $b$ and $c$ are non-zero constants. (a) It is given that $C$ passes through the point $left( 3,

2007 HCI P1 Q13 The curve $C$ has equation $y=frac{{{x}^{2}}+ax+4}{x+b}$.It is given that $C$ has vertical asymptote $x=-1$ and a stationary point at $x=2$. (i) Determine the values of $a$

2020 HCI Promo Q4 The curve $C$ is given by the equation $x(x+8)=4{{(y-2)}^{2}}-12$ Sketch $C$, indicating clearly the key features of the curve.[You are not required to give the coordinates