NTA Abhyas JEE Main2020MathematicsCirclePractice

The number of common tangents to the circles x 2 + y 2 + 2 x + 8 y - 23 = 0 and x 2 + y 2 - 4 x - 10 y + 9 = 0 , are

Correct answer

Step-by-step solution

The centres and radii of given circles are C 1 - 1 , - 4 , C 2 ( 2 , 5 ) and r 1 = 1 + 16 + 23 = 40 , r 2 = 4 + 25 - 9 = 20 Now, C 1 C 2 = 2 + 1 2 + 5 + 4 2 = 90 And r 1 + r 2 = 40 + 20 Here, C 1 C 2 < r 1 + r 2 ∴ Two common tangents can be drawn

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