NTA Abhyas JEE Main2020MathematicsHyperbolaPractice

The sum of the y -intercepts of the tangents drawn from the point - 2 , - 1 to the hyperbola x 2 3 - y 2 2 = 1 is

Correct answer

Step-by-step solution

Let, the equation of the tangent from - 2 , - 1 is y = m x + 3 m 2 - 2 ⇒ - 1 = - 2 m + 3 m 2 - 2 ⇒ 2 m - 1 2 = 3 m 2 - 2 ⇒ m 2 - 4 m + 3 = 0 ⇒ m = 1 , 3 So, the equations of the tangents are y + 1 = x + 2 & y + 1 = 3 x + 2 ⇒ y -intercepts of the tangents are 1 & 5 ⇒ the sum of y -intercepts = 6

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