Mathematics - Circle Question with Solution | TestHub

Let centre be $C(h,k)$ $CQ=CP=r$ $\Rightarrow C{Q}^2=C{P}^2$ $(h-0{)}^2+(k\pm 0{)}^2=C{M}^2+M{P}^2$ $h^2+(k\pm 2\mathrm{b}{)}^2=k^2+4a^2$ $h^2+k^2+4b^2\pm 4bk=k^2+4a^2$ Then, the locus of centre $C(h,k)$ $x^2+4b^2\pm 4by=4a^2$ Hence, the above locus of the centre of circle is a parabola.