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If the radical axis of the circles {x}^{{2}}+{y}^{{2}}+{2}{g}{

Question

If the radical axis of the circles $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and $2 x^{2} + 2 y^{2} + 3 x + 8 y + 2 c = 0$ touches the circle $x^{2} + y^{2} + 2 x + 1 = 0$ , show that either $g = \frac{3}{4}$ or $f = 2$

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If the radical axis of the circles

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

and

2 x^{2} + 2 y^{2} + 3 x + 8 y + 2 c = 0

touches the circle

x^{2} + y^{2} + 2 x + 1 = 0

, show that either

g = \frac{3}{4}

f = 2

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Question Text

If the radical axis of the circles

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

and

2 x^{2} + 2 y^{2} + 3 x + 8 y + 2 c = 0

touches the circle

x^{2} + y^{2} + 2 x + 1 = 0

, show that either

g = \frac{3}{4}

f = 2

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