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

Options

A. one pair of common tangents
B. only one common tangent
C. three common tangents
D. no common tangent

Answer

D

Explanation

The centres and radii of given circles are `C_(1)(0,0),r_(1)=4`
and `C_(2)(0,1), r_(2)=sqrt(0+1)=1.`
Now, `C_(1)C_(2)=sqrt(0+(0-1)^(2))=1`
and `r_(1)-r_(2)=4-1=3`
`:." "C_(1)C_(2)ltr_(1)-r_(2)`
Hence, second circle lies inside the first circle, so no common tangent is possible.