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The radical axis of the two distinct circles x2 + y2 + 2gx + 2fy + c = 0 and 2x2 + 2y2 + 4x + y + 2c = 0 touches the circle x2 + y2 − 4x − 4y + 4 = 0.

Then the centre of the circle x2 + y2 + 2gx + 2fy + c = 0 can be

Option: 1

\left ( -1,-2 \right )


Option: 2

\left ( -2,\frac{1}{2} \right )


Option: 3

\left ( -2,\frac{1}{4} \right )


Option: 4

\left ( -1,\frac{1}{4} \right )


Answers (1)

best_answer

The radical axis of given circles is

\mathrm{(2 g-2) x+\left(2 f-\frac{1}{2}\right) y=0}

This line is tangent to the circle \mathrm{x^2+y^2-4 x-4 y+4=0}

\mathrm{\begin{aligned} & \Rightarrow \text { either } g=1 \text { or } f=\frac{1}{4} \\ & \Rightarrow \text { either }\left(g=1 \text { and } f \neq \frac{1}{4}\right) \text { or }\left(g \neq 1 \text { and } f=\frac{1}{4}\right) \end{aligned}}

Posted by

Devendra Khairwa

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