Given Circle, x2+y2=4 &x2+y2−6x−8y=24 Centre of first circle is (0,0) Centre of second circle is (3,4) Distance between centre of two circle (0,0) to (3,4)=√(3−0)2+(4−0)2 √9+16=√25=5 Radius of first circle is 2 and radius of second circle is √(3)2+(4)2+24 =√25+24 =√49=7 R2−R1=C1C2 7−2=5
Where R2= Radius of Second Circle R1= Radius of First Circle C1C2= Distance between centre Here first circle touch second circle internally Hence, there is only one common tangent.