Number of common tangents of circles x^2 + y^2 - 8x - 2y + 1=0 and x^2 + y^2 +6x +8y=0 are?

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Please find below the solution to the asked query:

We havex2+y2-8x-2y+1=0Centre is C14,1Radius =r1=42+12-1=4x2+y2+6x+8y=0Centre is C2-3,-4Radius=r2=-32+-42-0=9+16=25=5C1C2=4+32+1+42=49+25=74Herer1+r2=4+5=9r2-r1=5-4=1As1<74<9r2-r1<C1C2<r1+r2Hence circle cut each other at two points, hence there will be twocommon tangents.

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