Question

The radius of the sphere $x^2+y^2+z^2-8x+12y-4z+k=0$ is $8$, then $k=$?

• A. $-8$
• B. $-6$
• C. $8$
• D. $6$

Answer 1

Answer: (A)

$-8$

Given equation of sphere is $x^2+y^2+z^2-8x+12y-4z+k=0$
$\Rightarrow (x-4{)}^2+(y+6{)}^2+(z-2{)}^2=56-k$
Given radius of sphere is $8$
$\Rightarrow 56-k=8^2$

$\Rightarrow k=-8$