Circles x^2 + y^2 - 2x - 4y = 0 and x^2 + y^2 - 8y - 4 = 0 - Vidyadip

MCQ

Circles ${x^2} + {y^2} - 2x - 4y = 0$ and ${x^2} + {y^2} - 8y - 4 = 0$

✓
Touch each other internally
B
Touch each other externally
C
Cuts each other at two points
D
None of these

✓

Answer

Correct option: A.

Touch each other internally

a
(a) ${C_1}(1,\;2),\;{C_2}(0,\;4),\;{R_1} = \sqrt 5 ,\;{R_2} = 2\sqrt 5 $

${C_1}{C_2} = \sqrt 5 $ and ${C_1}{C_2} = \;|{R_2} - {R_1}|$

Hence circles touch internally.

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