Question

The $C$artisian equation of the sphere with centre $(2,-1,3)$ and radius $5$ is

• A. $x^2+y^2+z^2-2x+2y-3z+5=0$
• B. $x^2+y^2+z^2+2x+y-3z-5=0$
• C. $x^2+y^2+z^2-4x+2y-6z-11=0$
• D. $x^2+y^2+z^2+4x-2y-3z-11=0$

Answer 1

The correct option is C $x^2+y^2+z^2-4x+2y-6z-11=0$

Using the standard equation of a sphere, i.e. $(x-x_1{)}^2+(y-y_1{)}^2+(z-z_1{)}^2=r^2$ where $(x_1,y_1,z_1)$ is the centre of the sphere and $r$ is the radius.
$\therefore$ here the equation becomes $(x-2{)}^2+(y+1{)}^2+(z-3{)}^2=5^2$
$\therefore x^2+y^2+z^2-4x+2y-6z-11=0$ becomes the answer.