Number of common tangents to circles {x^2} + {y^2} - x = 0,,{x^2} + {y^2} + x = 0 is

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10-1.Circle and System of Circles

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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

A

$2$

B

$1$

C

$4$

D

$3$

Solution

(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.

Standard 11

Mathematics

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