Show that the point (0, 9) is equidistant
from the points (-4,1) and (4.1)
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Answer:
Let P(x,y,z) be any point which is equidistant from A(0,2,3) and B(2,−2,1).
Then,
PA=PB
PA
2
=PB
2
(x−0)
2
+(y−2)
2
+(z−3)
2
=
(x−2)
2
+(y+2)
2
+(z−1)
2
4x−8y−4z+4=0
x−2y−z+1=0
Hence, the required locus is x−2y−z+1=0.
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