The number of common tangents to the circles and is
- A.1
- B.2
- C.3
- D.4
Show answer and solution
Correct option: C
Solution
Circle 1: centre (2, 3), radius = √(4+9+12) = 5
Circle 2: centre (-3, -9), radius = √(9+81-26) = 8
Distance between centres = √((2-(-3))² + (3-(-9))²) = √(25+144) = √169 = 13
Since d = 13 = r₁ + r₂ = 5 + 8, the circles are externally tangent to each other. For externally tangent circles, there are exactly 3 common tangents: 2 external tangents and 1 common internal tangent at the point of tangency.
Circle 2: centre (-3, -9), radius = √(9+81-26) = 8
Distance between centres = √((2-(-3))² + (3-(-9))²) = √(25+144) = √169 = 13
Since d = 13 = r₁ + r₂ = 5 + 8, the circles are externally tangent to each other. For externally tangent circles, there are exactly 3 common tangents: 2 external tangents and 1 common internal tangent at the point of tangency.
[JEE Main 2015]