First slide

Analysis of two circles in circles

Question

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

Moderate

A

one pair of common tangent
B

two pairs of common tangents
C

three common tangents
D

no common tangents

Solution

The circle $x^{2} + y^{2} - 2 y = 0$ is completely within $x^{2} + y^{2} = 16$ Hence, there is no common tangent.

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