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If S-=x^(2)+y^(2)+2gx=2fy+c=0 represents...

If `S-=x^(2)+y^(2)+2gx=2fy+c=0` represents a circle then show that the straight line `lx+my=n=0`
(i) touches the circle S=0 if
`g^(2)+f^(2)-c=(gl+mf-n)^(2)/(l^(2)+m^(2))`
(ii) meets the circle S=0 in two points if
`g^(2)+f^(2)-cgt((gl+mf-n)^(2))/(l^(2)+m^(2))`
(iii) will not meet the circle if
`g^(2)+f^(2)-clt((gl+mf-n)^(2))/(l^(2)+m^(2))`

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