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EEJ MAIN Mathematics QUESTION #6045
Question 1

Find the number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$.

  • 1
  • 2
  • 3✔️
  • 4
Correct Answer Explanation

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.