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The radical axis of the circles
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and $2 (x^{2} + y^{2}) + 3 x + 2 y + 2 c = 0$
touches the circle $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ , if

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g=43and f=2

g=43and f=12

g=−34and f=2

g=34 and f=12

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detailed solution

Correct option is B

The equation of radical axis is 2g−32x+(2f−1)y=0 (i)It touches the circle x2+y2+2x+2y+1=0∴−2g−32−(2f−1)2g−322+(2f−1)2=1⇒2g+2f−522=2g−322+(2f−1)2 Clearly , g=43 and f=12

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The radical axis of the circles x2+y2+2gx+2fy+c=0 and 2x2+y2+3x+2y+2c=0touches the circle x2+y2+2x+2y+1=0, if

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The radical axis of the circles
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and $2 (x^{2} + y^{2}) + 3 x + 2 y + 2 c = 0$
touches the circle $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ , if