Three Dimensional Geometry Question 247
Question: The co-ordinates of the points A and B are (2, 3, 4) (-2, 5,-4) respectively. If a point P moves so that $ PA^{2}-PB^{2}=k $ where k is a constant, then the locus of P is
Options:
A) A line
B) A plane
C) A sphere
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \because $ $ PA^{2}-PB^{2}=k $
$ \therefore $ $ [{{(x-2)}^{2}}+{{(y-3)}^{2}}+{{(z-4)}^{2}}] $
$ -[{{(x+2)}^{2}}+{{(y-5)}^{2}}+{{(z+4)}^{2}}]=k $ or $ -,8x+4y-16z-16=k $ , which is the equation of a plane.
BETA
