A common tangent T to the curves C1: x^2}/4 + y^2/9 = 1 and C2: {x^2}/{42} - {y^2}/{143} = 1 does not pass through the fourth quadrant. ​

Question

A common tangent T to the curves \(C_1 : \frac{x^2}4 + \frac{y^2}9 = 1\) and \(C_2: \frac{x^2}{42} - \frac{y^2}{143} = 1 \) does not pass through the fourth quadrant. If T touches C₁ at (x₁, y₁) and C₂ at (x₂, y₂), then |2x₁ + x₂| is equal to _______.

Answer 1

Let common tangents are

For given tangent not pass through 4^th quadrant