KCET2007MathematicsCircle

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

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Correct answer

B. 4

Step-by-step solution

Given, equation of circles are x²+y²=4 whose radius =2 centre =(0,0) and x²+y²-6 x-8 y-24=0 , whose radius = 9+16-24 = 1 =1 and centre =(3,4) Now, c₁ c₂= (3-0)²+(4-0)² = 9+16 =5 a₁+a₂=2+1=3 Since, c₁ c₂>a₁+a₂ Number of common tangents =4

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