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Question

# The coordinates of a point which is equidistant from the points (0,0,0),(a,0,0),(0,b,0)and(0,0,c) are given by _____

A

(a2,b2,c2)

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B

(a2,b2,c2)

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C

(a2,b2,c2)

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D

(a2,b2,c2)

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Solution

## The correct option is A (a2,b2,c2) Let that point be P(x,y,z) Given points A(0,0,0),B(a,0,0),C(0,b,0)andD(0,0,c) AP = BP = CP = DP AP2 = BP2 = CP2 = DP2 AP2=BP2 x2 + y2 + z2 = (x−a)2 + y2 + z2 ⇒ x2 = x2 + a2 − 2ax x = a2 similarly, AP2 = CP2 x2 + y2 + z2 =x2 + (x−b)2 + z2 y2 = y2 + b2 − 2by y=b2 and AP2 = DP2 x2 + y2 + z2 =x2 + y2 +(z−c)2 z2 = z2 + c2 − 2zc z = c2 ⇒ coordinate of the point C is (a2,b2,c2)

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