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Question

The coordinates of ends of one diameter of a sphere are (1,0,1) and (5,4,5). Find the equation, centre and diameter of sphere.

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Solution

Coordinates of end points of diameter of sphere are (1,0,1) and (5,4,5)
Equation of sphere
(xx1)(xx2)+(yy1)(yy2)+(zz2)(zz2)=0
(x1)(x5)+(y0)(y4)+(z1)(z5)=0
x25xx+5+y24y+z25zz+5=0
x2+y2+z26x4y6z+10=0
this is the equation to the required sphere
Coordinate of centre of sphere
Midpoint of diameter AB is O and centre of sphere is O
Coordinate of centre
(x=5+12,y=4+02,z=5+12)
(x=62,y=42,z=62)
(3,2,3)
Diameter of sphere = distance between points A and B
=(51)2+(40)2+(51)2=16×3=43
665778_628881_ans_f715fb14e9484f97b83e9affe2f21d17.png

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