If the line y = 2x + is a tangent to the hyperbola 36x^2 - 25y^2 = 3600 , then =

Step-by-step solution

The equation of the hyperbola is 36x^2 - 25y^2 = 3600 . Dividing by 3600 , we get: x^2 100 - y^2 144 = 1 Comparing with the standard equation x^2 a^2 - y^2 b^2 = 1 , we have a^2 = 100 and b^2 = 144 . The given line is y = 2x + . Comparing with y = mx + c , we have m = 2 and c = . The condition for a line to be tangent to a hyperbola is c^2 = a^2m^2 - b^2 . Substituting the values, we get: ^2 = 100(2)^2 - 144 ^2 = 400 - 144 ^2 = 256 = 16 Answer: 16