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Question

A line segment joining (1, 0, 1) and the origin (0, 0, 0) is revolved about the x-axis to form a right circular cone. If (x, y, z) is any point on the cone other than the origin, then it satisfies the equation


A

x22y2z2=0

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B

x2y2z2=0

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C

2x2y22z2=0

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D

x22y22z2=0

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Solution

The correct option is B

x2y2z2=0




Let A be the point (1,0,1) and P(x, y, z) be any point on the cone obtained revolving OA about the x-axis.
From the figure,
ΔOPM and ΔOAC are similarOPOA=OMOCx2+y2+z22=x1x2+y2+z2=2x2x2y2z2=0


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