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Question

The locus of center of a circle which passes through the origin and cut off a length of 4 units from the line x=3is


A

y2+6x=0

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B

y2+6x=13

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C

y2+6x=10

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D

x2+6y=13

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Solution

The correct option is B

y2+6x=13


Explanation for correct option

Let the circle be C-g,-f, then the equation of the line passing through origin is x2+y2+2gx+2fy=0

Distance, d=CA=-g-3=g+3

In ABC,

Using distance formula, for points x1,y1 and x2,y2

d=x2-x12+y2-y22

BC2=OC2=0-g2+0-f22=f2+g2AC2=g+32+f-f22=(g+3)2BA2=g+3-(g+3)2+(f+2-f)22=22

BC2=AC2+AB2 [ Pythagoras theorem ]

f2+g2=(g+3)2+4f2+g2=g2+9+6g+4f2=6g+13f2-6g-13=0

Eliminating -f=y,-g=x

y2+6x=13

Hence, option B is correct.


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