Number of common tangents to circles x^2 + y^2 -2x + 4y -4 = 0 and x^2 + y^2 -8x -4y + 16 = 0 is-

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10-1.Circle and System of Circles

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Number of common tangents to the circles
$x^2 + y^2 -2x + 4y -4 = 0$ and
$x^2 + y^2 -8x -4y + 16 = 0 $ is-

A

$0$

B

$2$

C

$3$

D

$4$

Solution

${C_1} \equiv \left( {1, – 2} \right),{r_1} = 3$

${C_2} \equiv \left( {4,2} \right),{r_2} = 2$

$\left| {{C_1}{C_2}} \right| = 5 = {r_1} + {r_2}$

$ \Rightarrow 3$ tangents

Standard 11

Mathematics

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