2015/078) Find the equation of the sphere passing $(a,0,0), (0,b,0), (0,0,c)$ and $(0,0,0)$

the general equation of sphere

$x^2+y^2+z^2+mx +ny + rz = p^2$

as it passes through $(0,0,0)$ put $(x,y,z) = (0,0,0)$ to get $p^2 = 0$ or $p = 0$

as it passes through $(a,0,0)$ put $(x,y,z) = (a,0,0)$ to get $a^2 + ma = 0$ or $m = -a$

similarly $n = -b$ and $r = -c$ and we get equation as

$x^2+y^2+z^2 - ax - by - cz = 0$