What is the distance between the two foci of the hyperbola 25x^2 - 75y^2 = 225 ?

Step-by-step solution

The given equation of the hyperbola is 25x^2 - 75y^2 = 225 . Dividing the entire equation by 225 , we get: x^2 9 - y^2 3 = 1 Comparing this with the standard equation of a hyperbola x^2 a^2 - y^2 b^2 = 1 , we have a^2 = 9 and b^2 = 3 . The relation between a , b , and the distance from the center to a focus c is given by c^2 = a^2 + b^2 . Substituting the values, we get: c^2 = 9 + 3 = 12 c = 12 = 2 3 The distance between the two foci is 2c . Distance = 2(2 3 ) = 4 3 units. Answer: 4 3 units