Three Dimensional Geometry Question 15
Question: The equation of a sphere is $ x^{2}+y^{2}+z^{2}-10z=0 $ . If one end point of a diameter of the sphere is (-3, -4, 5), what is the other end point?
Options:
A) $ (-3,-4,-5) $
B) $ (3,4,5) $
C) $ (3,4,-5) $
D) $ (-3,4,-5) $
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Answer:
Correct Answer: B
Solution:
[b] The equation of the given sphere is $ x^{2}+y^{2}+z^{2}-10z=0. $
$ \therefore $ Its centre is (0, 0, 5). Coordinates of one end point of a diameter of the sphere is given as (-3, -4, 5). Let coordinates of another end point of this diameter $ (x_1,y_1,z_1) $
$ \therefore \frac{-3+x_1}{2}=0\Rightarrow x_1=3 $ $ \frac{-4+y_1}{2}=0\Rightarrow y_1=4 $ and $ \frac{5+z_1}{2}=5,\Rightarrow z_1=5 $
$ \therefore $ Required coordinates are (3, 4, 5).
BETA
