Year 11 Maths - Specialist Graphing techniques

Locus of points

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Questions

Question 1

58618

Find the locus of points $P(x,y)$ whose distance from $Q(-2,3)$ is $3$ units.

Answer

$(x+2)^2+(y-3)^2=9$

Worked Solution

$$\begin{aligned}
&\text{This is a circle of the form}\\
&(x-h)^{2} \leftarrow(y-k)^{2}=r^{2}\\
&\text{with centre (h,k) and radius r}\\
&\therefore\ Q(-2,3)\ \text{is the centre and}\ r=3\ \text{the radius}\\
&\therefore\ \text{The locus is}\ (x+2)^{2}+(y-3)^{2}=9\\
\end{aligned}$$

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