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COMEDK2020MathematicsCircle

The number of common tangents to the circles x²+y²=4 and x²+y²-6 x-8 y-24=0 is,

Options

  1. A4
  2. B3
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

We have, Equation of circle is x²+y²=4 . Its centre is C₁(0,0) and radius (r₁ ) is 2 . Equation of another circle is x²+y²-6 x-8 y-24=0 i.e. (x-3)²+(y-4)²= 7)² . Its centre is C 2(3,4) and radius r₂ is 7 . Nos, C₁ C_ g = (3-0)²+(4-0)² =5 and |n₁-r₂ |=|2-7|=5 C₁ C₂= |r₁-r₂ | So, both circles touch each other internally.

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