Find the inner common tangent equations of two circles X & # 178; + Y & # 178; = 16 and (x-3) + (y + 4) &# 178; = 1

Find the inner common tangent equations of two circles X & # 178; + Y & # 178; = 16 and (x-3) + (y + 4) &# 178; = 1

O(0,0),O1(3,-4),R1=√(16)=4 R2=√(1)=1
|OO1|=√((3^2)+((-4)^2))=5=R1+R2
Two circles circumscribed
First, find the oo1 equation: k = (- 4-0) / (3-0) = - 4 / 3
y=-4/3•x
The inner common tangent is perpendicular to oo1, K1 = 3 / 4
Calculate the P coordinate of the tangent point
X & # 178; + Y & # 178; = 16 ((x-3) ^ 2) + (y + 4) &# 178; = 1 simultaneous x = 12 / 5, y = - 16 / 5
The inner common tangent equation (y + 16 / 5) = 3 / 4 (X-12 / 5)
4x-3y+20=0