(D) For the circle $x^2+y^2=16$, the center $C_1$ is $(0,0)$ and the radius $r_1 = 4$. For the circle $x^2+y^2-2y=0$, the center $C_2$ is $(0,1)$ and

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(D) For the circle $x^2+y^2=16$, the center $C_1$ is $(0,0)$ and the radius $r_1 = 4$. For the circle $x^2+y^2-2y=0$, the center $C_2$ is $(0,1)$ and the radius $r_2 = \sqrt{0^2+1^2} = 1$. The distance between the centers $C_1$ and $C_2$ is $d = \sqrt{(0-0)^2 + (1-0)^2} = 1$. We compare the distance $d$ with the radii: $r_1 - r_2 = 4 - 1 = 3$. Since $d Therefore, there are no common tangents between the 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:

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A
one pair of common tangents
B
only one common tangent
C
three 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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For the two circles $x^2+y^2=16$ and $x^2+y^2-2y=0$, there is/are:

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