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  • The equation of a circle of radius 1 touching the circles is<div class='qna-

The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|=0 is

Option: 1

x^2+y^2+2 \sqrt{3} x-2=0


Option: 2

x^2+y^2-2 \sqrt{3} y+2=0


Option: 3

x^2+y^2+2 \sqrt{3} y+2=0


Option: 4

x^2+y^2+2 \sqrt{3} x+2=0


Answers (1)

best_answer

The given circles are x^2+y^2-2 x=0, x>0 , and x^2+y^2+2 x=0, x<0 .

From the figure, the centres of the required circles will be (0, \sqrt{3}) and (0,-\sqrt{3}) .

\therefore The equations of the circles are (x-0)^2+\left(y[\sqrt{3})^2=1^2 .\right.

\begin{aligned} & \Rightarrow x^2+y^2+3-2 \sqrt{3} y=1 \\\\ & \Rightarrow \quad x^2+y^2-2 \sqrt{3} y+2=0 \end{aligned}

Posted by

Ritika Kankaria

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