Question

The sphere $x^2+y^2+z^2-2x+4y+6z+1=0$ touches.

• A. $x$-axis
• B. $y$-axis
• C. $z$-axis
• D. All

Answer 1

The correct option is A $x$-axis

Given, $x^2+y^2+z^2-2x+4y+6z+1=0$
Centre of the sphere is $(1,-2,-3)$ and radius $=\sqrt{1^2+2^2+3^2-1}=\sqrt{13}$
Now distance of centre of the sphere from $x$-axis, $y$-axis and $z$-axis are $\sqrt{2^2+3^2}=\sqrt{13},\sqrt{1^2+3^2}=\sqrt{10}$
and $\sqrt{1^2+2^2}=\sqrt{5}$ respectively.
Clearly, sphere touches $x$-axis.