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Consider the circles S(1):x^(2)+y^(2)-...

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.

Text Solution

Verified by Experts

The correct Answer is:
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`
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