Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

# What is the equation of a sphere in standard form?

The answer is: x^2+y^2+z^2+ax+by+cz+d=0,

This is because the sphere is the locus of all points P(x,y,z) in the space whose distance from C(x_c,y_c,z_c) is equal to r.

So we can use the formula of distance from P to C, that says:

sqrt((x-x_c)^2+(y-y_c)^2+(z-z_c)^2)=r and so:

(x-x_c)^2+(y-y_c)^2+(z-z_c)^2=r^2,

x^2+2(x)(x_c) + x_c^2+y^2+2(y)(y_c)+y_c^2+z^2+2(z)(z_c)+z_c^2=r^2,

x^2+y^2+z^2+ax+by+cz+d=0,

in which

a=2x_c; b=2y_c; c=2z_c; d=x_c^2+y_c^2+z_c^2-r^2;

So:

C(-a/2,-b/2,-c/2)

and r, if it exists, is:

r=sqrt(x_c^2+y_c^2+z_c^2-d).

If the center is in the Origin, than the equation is:

x^2+y^2+z^2=r^2,