Question

Consider the circles
`S_(1):x^(2)+y^(2)-4x-6y-12=0`
and `S_(2):x^(2)+y^(2)+6x+18y+26=0`
then which of the following is (are) correct?
A. The circles `S_(1)" and "S_(2)` touches each other.
B. Number of common tangent(s) to `S_(1)" and "S_(2)` is 1.
C. The equation of radical axis of `S_(1)" and "S_(2)" is "5x+12y+19=0`.
D. Circle `S_(2)` neither touches nor cuts the coordinate axes.

Answer 1

Correct Answer - A
Circles touch externally as `C_(1)C_(2)=r_(1)+r_(2).`
`C_(1)(2,3)," "r_(1)=5`
`C_(2)(-3,-9)," "r_(2)=8`