(D) For the circle $x^2 + y^2 = 16$,the center $C_1 = (0, 0)$ and radius $r_1 = 4$.For the circle $x^2 + y^2 - 2y = 0$,we rewrite it as $x^2 + (y - 1)

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(D) For the circle $x^2 + y^2 = 16$,the center $C_1 = (0, 0)$ and radius $r_1 = 4$.For the circle $x^2 + y^2 - 2y = 0$,we rewrite it as $x^2 + (y - 1)^2 = 1$,so the center $C_2 = (0, 1)$ and radius $r_2 = 1$.The distance between the centers is $d = \sqrt{(0 - 0)^2 + (1 - 0)^2} = 1$.The sum of the radii is $r_1 + r_2 = 4 + 1 = 5$.The difference of the radii is $|r_1 - r_2| = |4 - 1| = 3$.Since $d Therefore,there are no common tangents to these two circles.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

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For the two circles $x^2 + y^2 = 16$ and $x^2 + y^2 - 2y = 0$,there is/are:

JEE MAIN 2014 All JEE MAIN

A
one pair of common tangents
B
two pairs of common tangents
C
three pairs of common tangents
D
no common tangent

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

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