For given circles {x^2} + {y^2} - 6x - 2y + 1 = 0 and {x^2} + {y^2} + 2x - 8y + 13 = 0 , which of fo

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10-1.Circle and System of Circles

medium

For the given circles ${x^2} + {y^2} - 6x - 2y + 1 = 0$ and ${x^2} + {y^2} + 2x - 8y + 13 = 0$, which of the following is true

A

One circle lies inside the other

B

One circle lies completely outside the other

C

Two circle intersect in two points

D

They touch each other

Solution

(d) ${C_1} = (3,\;1),\;{C_2}( – 1,\;4),$

${R_1} = 3,\;{R_2} = 2$

${C_1}{C_2} = \sqrt {16 + 9} = 5,$

${R_1} + {R_2} = {C_1}{C_2}$

Hence circles touch externally.

Standard 11

Mathematics

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