Question Number 8756 by trapti rathaur@ gmail.com last updated on 25/Oct/16
$${show}\:{that}\:{every}\:{sphere}\:{through}\:{the}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{ax}+{r}^{\mathrm{2}} =\mathrm{0},{z}=\mathrm{0} \\ $$$$,{z}=\mathrm{0}\:\:\:\:\:\:\:{cuts}\:{orthogonally}\:{every}\:{sphere}\:{through}\:{the}\:{circle}\: \\ $$$${x}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} ,\:{y}={o}\:. \\ $$