Three Dimensional Geometry Question 26
Question: The centre of sphere passes through four points (0, 0, 0), (0, 2, 0), (1, 0, 0) and (0, 0, 4) is
[MP PET 2002]
Options:
A) $ ( \frac{1}{2},,1,,2 ) $
B) $ ( -\frac{1}{2},,1,,2 ) $
C) $ ( \frac{1}{2},,1,-,2 ) $
D) $ ( 1,\frac{1}{2},,2 ) $
Show Answer
Answer:
Correct Answer: A
Solution:
Let the equation of sphere $ x^{2}+y^{2}+z^{2}+2ux+2vy+2wz+d=0 $ $ \because $ It passes through origin (0, 0, 0), \ $ d=0 $ Also, it passes through (0, 2, 0) \ $ 4+4v=0\Rightarrow v=-1 $ Also, it passes through (1, 0, 0) \ $ 1+2u=0\Rightarrow u=-1/2 $ And it passes through (0, 0, 4) \ $ 16+8w\Rightarrow w=-2 $ \ Centre $ (-u,,-v,,-w)=( \frac{1}{2},,1,,2 ) $ .
BETA
