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The number of common tangents to the circles $x^2+y^2-x=0, x^2+y^2+x=0$ is
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$3$
The centres and radii of the circles are Centres: $C_1\left(\frac{1}{2}, 0\right), C_2\left(-\frac{1}{2}, 0\right)$
Radii: $r_1=\frac{1}{2}, r_2=\frac{1}{2}$
Clearly, $C_1 C_2=r_1+r_2$. Therefore the circles touch each other externally. Hence there are $3$ common tangents.
Radii: $r_1=\frac{1}{2}, r_2=\frac{1}{2}$
Clearly, $C_1 C_2=r_1+r_2$. Therefore the circles touch each other externally. Hence there are $3$ common tangents.
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