The locus of the centere of a circle which passes through the point (0,0) and cuts off a length 2b from the line x=c is-

Options

A. `y^(2)+2cx=b^(2)+c^(2)`
B. ` x^(2)+cx=b^(2)+c^(2)`
C. ` y^(2)+2cy=b^(2)+c^(2)`
D. none of these

Answer

A

Explanation

Let the centre of circle
`C(x_(1),y_(1))`
As it passes through (0,0)
its radius `OC=sqrt((x_(1)^(2)-y_(1)^(2)))`
`CB=r=sqrt(x_(1)^(2)-y_(1)^(2))`
CM= length of `_|_` from C on line x-c=0
` CM|(x_(1)-c)/(sqrt(1))|`
in `DeltaBCM`
`rArrb^(2)=CB^(2)-CM^(2)`
`rArrb^(2)=x_(1)^(2)+y_(1)^(2)-(x_(1)-c)^(2)`
`rArr:.` locus `y^(2)+2cx=b^(2)+c^(2)`