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Statement 1 : If two circles {x}^{{2}}+{y}^{{2}}+{2}{g}{x}+{2}

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Statement 1 : If two circles $x^{2} + y^{2} + 2 g x + 2 f y = 0$ and $x^{2} + y^{2} + 2 g^{p r i m e} x + 2 f^{p r i m e} y = 0$ touch each other, then $f^{p r i m e} g = f g^{p r i m e} ˙$ Statement 2 : Two circles touch other if the line joining their centers is perpendicular to all possible common tangents.

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Statement 1 : If two circles

x^{2} + y^{2} + 2 g x + 2 f y = 0

and

x^{2} + y^{2} + 2 g^{p r i m e} x + 2 f^{p r i m e} y = 0

touch each other, then

f^{p r i m e} g = f g^{p r i m e} ˙

Statement 2 : Two circles touch other if the line joining their centers is perpendicular to all possible common tangents.

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Question Text

Statement 1 : If two circles

x^{2} + y^{2} + 2 g x + 2 f y = 0

and

x^{2} + y^{2} + 2 g^{p r i m e} x + 2 f^{p r i m e} y = 0

touch each other, then

f^{p r i m e} g = f g^{p r i m e} ˙

Statement 2 : Two circles touch other if the line joining their centers is perpendicular to all possible common tangents.

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