Question

The equation of the sphere touching the three coordinates planes is

• A. $\sum x^2+2a(x+y+z)+2a^2=0$
• B. $\sum x^2-2a(x+y+z)+2a^2=0$
• C. $\sum x^2\pm 2a(x+y+z)+2a^2=0$
• D. $\sum x^2\pm 2ax\pm 2ay\pm 2az+2a^2=0$

Answer 1

The correct option is D $\sum x^2\pm 2ax\pm 2ay\pm 2az+2a^2=0$

Let the radius of the sphere be $a;$ then the distance of its center from coordinate planes which it is touching should be equal to radius $a$.

Hence, its center is $(a,a,)$.

But since the center can be in any octant, we say that its center is $(\pm a,\pm a,\pm a)$ and radius $a$, so that its equation is

${(x\pm a)}^2+{(y\pm a)}^2+{(z\pm a)}^2=a^2\Rightarrow x^2+y^2+z^2\pm 2ax\pm 2ay\pm 2az+2a^2=0$