The number of common tangents to the circles x^2+y^2-18x-15y+131=0 and x^2+y^2-6x-6y-7=0 i…

Question

The number of common tangents to the circles $x^2+y^2-18x-15y+131=0$ and $x^2+y^2-6x-6y-7=0$ is:

Accepted Answer

$C_1=(9,7.5),\ r_1=\sqrt{81+56.25-131}=2.5$. $C_2=(3,3),\ r_2=\sqrt{9+9+7}=5$.

$$C_1C_2=\sqrt{36+20.25}=7.5=r_1+r_2,$$

so the circles are externally tangent, giving 3 common tangents.

Solutions · 1