Mathematics - Circle Question with Solution | TestHub

Let $\mathrm{P}(\mathrm{x},\mathrm{y})$ be the point dividing the join of $\mathrm{A}$ and $\mathrm{B}$ in the ratio 2: 3 internally, then $$\begin{array}{c}\mathrm{x}=\frac{20\cos \theta +15}{5}=4\cos \theta +3\Rightarrow \cos \theta =\frac{\mathrm{x}-3}{4}\\ \mathrm{y}=\frac{20\sin \theta +0}{5}=4\sin \theta \Rightarrow \sin \theta =\frac{\mathrm{y}}{4}\dots \text{ (ii) }\end{array}$$ Squaring and adding (i) and (ii), we get the required locus $(x-3{)}^2+y^2=16,$ which is a circle.