Find the equation of the sphere having extremities of one of its diameters as the
points (2,3, 5) and (-4, 7,11).
A
x2+y2+z2−2x−10y−16z+68=0
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B
x2+y2+z2+2x−10y−16z=68
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C
x2+y2+z2+2x−10y−16z+68=0
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D
x2+y2+z2+2x+10y+16z+68=0
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Solution
The correct option is Cx2+y2+z2+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 x2+y2+z2+2x-10y -16z +68 =0