Three Dimensional Geometry Question 43
Question: If (2, 3, 5) is one end of a diameter of the sphere $ x^{2}+y^{2}+z^{2}-6x-12y-2z+20=0 $ then co-ordinates of the other end of the diameter are
[Kerala (Engg.) 2005]
Options:
A) (4, 3, 5)
B) (4, 9, -3)
C) (4, 9, 3)
D) (4, 3, -3)
E) (4, 9, 5)
Show Answer
Answer:
Correct Answer: B
Solution:
Equation of sphere is, $ x^{2}+y^{2}+z^{2}-6x-12y-2z+20=0 $ Centre of sphere $ =(3,6,1) $ and one end of circle = $ (2,,3,,5) $ Let other end be $ (x,y,z) $
$ \therefore $ $ \frac{2+x}{2}=3,\frac{3+y}{2}=6,,\frac{5+z}{2}=1 $
Þ $ x=6-2 $ , $ y=12-3 $ , $ z=2-5 $
Þ $ x=4,y=9,z=-3 $ Hence, other end is (4, 9, ?3).
BETA
