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Find the number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$.
Circle 1: centre $C_1=(2,3)$, $r_1=\sqrt{4+9+12}=5$.
Circle 2: centre $C_2=(-3,-9)$, $r_2=\sqrt{9+81-26}=8$.
Distance $|C_1C_2|=\sqrt{(2+3)^2+(3+9)^2}=\sqrt{25+144}=\sqrt{169}=13$.
Since $|C_1C_2|=13=r_1+r_2=5+8$, the circles are externally tangent. Externally tangent circles have exactly 3 common tangents.
The Lady Health Worker (LHW) Programme was officially launched in 1994 in Pakistan. It was established under the National Programme for Family Planning and Primary Health Care. LHWs serve as the backbone of community health in Pakistan, each covering a population of approximately 1,000 persons (around 150β200 households). As a Charge/Head Nurse, understanding the origin and scope of this programme is critical for effective community nursing management.
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