Mathematics - Circle Question with Solution | TestHub

Let the centre be $(\alpha ,\beta )$ $\because$ It cut the circle ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{p}}^2$ orthogonally $2(-\alpha )\times 0+2(-\beta )\times 0=c_1-p^2$ ${\mathrm{c}}_1={\mathrm{p}}^2$ Let equation of circle is $x^2+y^2-2\alpha x-2\beta y+p^2=0$ It pass through $(a,b)\Rightarrow a^2+b^2-2\alpha a-2\beta b+p^2=0$ Locus $\therefore 2ax+2by-\left(a^2+b^2+p^2\right)=0$