Question

Find the equation of the sphere having extremities of one of its diameters as the
points (2,3, 5) and (-4, 7,11).

• A. $x^2+y^2+z^2-2x-10y-16z+68=0$
• B. $x^2+y^2+z^2+2x-10y-16z=68$
• C. $x^2+y^2+z^2+2x-10y-16z+68=0$
• D. $x^2+y^2+z^2+2x+10y+16z+68=0$

Answer 1

The correct option is C $x^2+y^2+z^2+2x-10y-16z+68=0$

Equation of a sphere having extremities of one of its diameters as (a, b, c) and (p, q, r) is (x - a)(x - p) + (y - b)(y - q) + (z - c)(z - r) = 0
The required equation of the sphere is
(x - 2)(x + 4) + (y - 3)(y - 7) + (z - 5)(z - 11) = 0
or $x^2+y^2+z^2$+2x-10y -16z +68 =0