For the given circles `x^(2)+y^(2)-6x-2y+1=0` and `x^(2)+y^(2)+2x-8y+13=0`, which of the following is true?

Options

A. One circle lies inside the other
B. One circle lies completely outside the other
C. Two circles intersection in two points
D. They touch each other externally

Answer

D

Explanation

The centres of the given circles are `C_(1) (3, 1)` and `C_(2)(-1, 4)` and corresponding radii are `r_(1)=sqrt(3^(2)+1^(2)-1)=3`
and `r=sqrt((-1)^(2)+4^(2)-13)=2` respectively.
Now, `C_(1)C_(2)=sqrt((3+1)^(2)+(1-4)^(2))=5`
Clearly, `C_(1)C_(2)=r_(1)+r_(2)`
So, given circles touch each other externally.