Year 11 Maths - Specialist Graphing techniques

Hyperbolas

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Questions

Question 1

58647

Sketch the graph of $(x+1)^2-(y-1)^2=1$. Find

i) the coordinates of the centre

ii) the equations of the asymptotes

Answer

i) Centre = $(-1,1)$ ii) $y=x+2,\,y=-x$

Worked Solution

$$
\begin{aligned}
&(x+1)^{2}-(y-1)^{2}=1\\
&\text{is an hyperbola}\\
&\text{of the form}\\
&(x-n)^{2}-(y-k)^{2}=1\\
&\text{where}\ (n, k) \text{is}\\
&\text{The centre}\\
&\text{let}\ (x-h)^{2}=(n-k)^{2}\\
&\text{to locate the}\\
&\text{asymptotes}\\
&\begin{array}{c}
\therefore \quad y-k=\pm(x-h) \\
y=k \pm(x-n)
\end{array}\\
&\therefore \text{cantue is}\ (-1,1)\\
&\begin{array}{l}
y=1 \pm(x+1) \\
y=x+2, y=-x
\end{array}
\end{aligned}
$$

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