I know how to find the equation of a sphere when four points, through which it passes is given. But here I'm unable to find coordinates of points $A, B, C$ in terms of $p, q, r.$


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    $\begingroup$ Please check the question: it should be p/x + q/y + r/z = 2 $\endgroup$ – PTDS Apr 15 at 6:14
  • $\begingroup$ You don't need to express $A,B,C$ in terms of $p,q,r$. Write the equation of the plane through $(p,q,r)$ whose normal vector is $(a,b,c)$, calculate $A,B,C$ in terms of $p,q,r,a,b,c$ and then find the center $(x,y,z)$ of the sphere. Then notice that $p/x+q/y+r/z=2$ (I agree with PTDS that it should be $2$) independently from $a,b,c$. $\endgroup$ – SMM Apr 15 at 8:02
  • $\begingroup$ I confirm it's p/x + q/y + r/z = 0 $\endgroup$ – Manas Apr 16 at 7:54
  • $\begingroup$ Can anyone give me complete solution $\endgroup$ – Manas Apr 16 at 7:55