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Question
Equation to the sphere passing through the circle x2+y2+z2=9, x+3y+4z=5
and the point (1,2,3) is
Equation to the sphere passing through the circle x2+y2+z2=9, x+3y+4z=5
and the point (1,2,3) is
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Solution
The correct option is C None of These
Equation of sphere passes through circle x2+y2+z2=9, x+3y+4z=5 is given by,
x2+y2+z2−9+λ(x+3y+4z−5)=0
Also given it passes through (1,2,3)
⇒(1+4+9−9)+λ(1+6+12−5)⇒λ=−514
Hence, required sphere is 14(x2+y2+z2)−5x−15y−20y−121=0.
Equation of sphere passes through circle x2+y2+z2=9, x+3y+4z=5 is given by,
x2+y2+z2−9+λ(x+3y+4z−5)=0
Also given it passes through (1,2,3)
⇒(1+4+9−9)+λ(1+6+12−5)
⇒λ=−514
Hence, required sphere is 14(x2+y2+z2)−5x−15y−20y−121=0.
Hence, required sphere is 14(x2+y2+z2)−5x−15y−20y−121=0.
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