The number of common tangents to the circles | vedclass

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Question

(d) The centres and radii of the circles are

Centres : ${C_1}\left( {\frac{1}{2},\;0} \right)\,\,,\;{C_2}\left( { - \frac{1}{2},\;0} \right)$

Ra

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(d) 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.

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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