TS EAMCET 4-Aug-2021 Shift 1 Question Paper

Let S1≡x2+y2+4x−6y−3=0
⇒‌‌g‌‌=2,f=−3,C1=−3
[∵r=√g2+f2−c‌ and centre ‌=(−g,−f)]
Centre, C1(−2,3)
radius, r1=√(−2)2+32+3=4
and S2≡x2+y2+4x−2y+1=0
⇒g2=2,f2=−1,C2=1Centre, C2(−2,1)
Radius, r2=√(−2)2+12−1=2
Distance between centres C1C2=√02+22=2
Difference in radius |r1−r2|=2
∵C1C2=|r−r2|
∴ Circle touches each other internally at one point
⇒ Number of tangents =1