Three Dimensional Geometry Question 335
Question: If the plane $ 2ax-3ay+4az+6=0 $ passes through the midpoint of the line joining the centres of the spheres $ x^{2}+y^{2}+z^{2}+6x-8y-2z=13 $ and $ x^{2}+y^{2}+z^{2}-10x+4y-2z=8 $ then a equals
Options:
A) -1
B) 1
C) -2
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Plane $ 2ax-3ay+4az+6=0 $ passes through the midpoint of the centre of spheres $ x^{2}+y^{2}+z^{2}+6x-8y-2z=13 $ and $ x^{2}+y^{2}+z^{2}-10x+4y-2z=8 $ Respectively center of spheres are $ (-3,4,1) $ and $ (5,-2,1). $ Midpoint of centres is $ (1,1,1). $ Satisfying this in the equation of plane, we get $ 2a-3a+4a+6=0\Rightarrow a=-2. $
BETA
