Question

The intersection of the spheres $x^2+y^2+z^2+7x-2y=13$ and $x^2+y^2+z^2-3x+3y+4z=8$ is the same as the intersection of one of the spheres and the plane

• A. $x-y-\frac{4z}{5}=1$
• B. $x-2y-z=1$
• C. $x-y-2z=1$
• D. $2x-y-\frac{4z}{5}=1$

Answer 1

The correct option is D $2x-y-\frac{4z}{5}=1$

The equation of the plane will be the equation of the plane at the intersection of the two sphere which is given by $S_2-S_1=0$
$x^2+y^2+z^2+7x-2y-13-(x^2+y^2+z^2-3x+3y+4z-8)=0$
$\Rightarrow 10x-5y-4z=5$
$\Rightarrow 2x-y-\frac{4z}{5}=1$