Three Dimensional Geometry Question 380
Question: A plane passes through a fixed point (a, b, c). The locus of the foot of the perpendicular to it from the origin is the sphere
Options:
A) $ x^{2}+y^{2}+z^{2}-ax-by-cz=0 $
B) $ x^{2}+y^{2}+z^{2}-2ax-2by-2cz=0 $
C) $ x^{2}+y^{2}+z^{2}-4ax-4by-4cz=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let (a, b, c) be the fixed point on the variable plane Now D. R?s of OM are $ x-0,y-0,z-0 $ i.e x, y, z D.R.?s of MA are x-a, y-b, z-c. Since OM perpendicular Ma $ x(x-a)+y(y-b)+z(z-c)=0 $
$ \Rightarrow x^{2}+y^{2}+z^{2}-ax-by-cx=0 $
BETA
