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  4. Equation of a circle which passes through origin and has center on x+y-1=0 given that its length of tangent from (1,2) is 1 is.

Q. Equation of a circle which passes through origin and has center on $x+y-1=0$ given that its length of tangent from $(1,2)$ is $1$ is_____.

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Solution:

given $\Rightarrow c=0\, \&\,-g-f-1=0$
$\therefore g+f=-1$
$l=\sqrt{s} \Rightarrow 1=1+4+2 g+4 f+c \ldots \ldots . .(1)$
$\therefore 2 g+4 f=-4 \Rightarrow g+2 f=-2 \ldots \ldots \ldots . .(2)$
(1) & (2)
$\Rightarrow-f=1$
$\therefore f=-1: g=-1-f=-1+1=0$
$\therefore$ R.E. is $x^{2}+y^{2}-2 y=0$

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