Match the items of Column-I with those of Column-II.
Column-I | Column-II | ||
(I) | The equation of the locus of a point whose distance from the -axis is equal to its distance from the xy plane is | (P) | + |
(II) | The equation of the sphere with centre at and touching yz-plane is | (Q) | |
(III) | The equation of the locus of the point whose distance from is 4 is | (R) | |
(IV) | The equation of the locus of the point whose distance from the y-axis is equal to its distance from the point ( ) is | (S) |
; 
; (III) 
; (IV) 
; 
; (III) 
; (IV) 
; 
; (III) 
; 
Text Solution
Verified by ExpertsA
(I) The distance of a point from z-axis is 
.
The distance of the point from xy-plane is 
. Therefore
(II) Since the sphere touches yz-plane, its radius is 
. Hence, the equation of the sphere is
(III) The locus is
(IV) We have
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