The number of common tangents to the circles | vedclass

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Question

(b) Circles ${S_1} \equiv {x^2} + {y^2} = {2^2}$,

${S_2} \equiv {(x - 3)^2} + {(y - 4)^2} = {7^2}$

$	herefore $ Centres ${C_1} = (0,\;0),$ ${C_

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(b) Circles ${S_1} \equiv {x^2} + {y^2} = {2^2}$,

${S_2} \equiv {(x - 3)^2} + {(y - 4)^2} = {7^2}$

$	herefore $ Centres ${C_1} = (0,\;0),$ ${C_2} = (3,\,4)$

and radii ${r_1} = 2,\;{r_2} = 7$

$	herefore \;{C_1}{C_2} = 5,$  ${r_2} - {r_1} = 5$

$i.e$., circles touch internally.

Hence there is only one common tangent.

The number of common tangents to the circles ${x^2} + {y^2} = 4$ and ${x^2} + {y^2} - 6x - 8y = 24$ is

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