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A line segment joining (1,0,1) and the o...

A line segment joining (`1,0,1)` and the origin `(0,0,0)` is resolved 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

`x^(2)-2y^(2)-z^(2)=0`

B

`x^(2)-y^(2)-z^(2)=0`

C

`2x^(2)-y^(2)-2z^(2)=0`

D

`x^(2)-2y^(2)-2z^(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
B
`triangleOPM` and `triangleOAC` are similar

`(OP)/(OA) = (OM)/(OC`
`sqrt(x^(2)+y^(2)+z^(2))/sqrt(2) = x/1`
`rArr x^(2)+y^(2)+z^(2)=x/1`
`rArr x^(2)-y^(2)-z^(2)=0`
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