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The two circles $x^{2} + y^{2} - 5 = 0$ and $x^{2} + y^{2} - 2 x - 4 y - 15 = 0$

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touch each other externally

touch each other internally

cut each other orthogonally

do not intersect

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detailed solution

Correct option is B

Coordinates of the centres of the two circles are C1(0,0), C2(1,2) and their radii are r1=5,r2=25.We have, C1C2=5=r2−r1.Hence, the two circles touch each other internally.

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The two circles x2+y2−5=0 and x2+y2−2x−4y−15=0

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The two circles $x^{2} + y^{2} - 5 = 0$ and $x^{2} + y^{2} - 2 x - 4 y - 15 = 0$