A variable chord of the hyperbola subtends a right angle at the centre of the hyperbola. If this chord touches a fixed circle which is concentric with the hyperbola and r is the radius of the circle, then ________.
1) the equation of the hyperbola is x²/a² - y²/b² = 1
2) the equation of the hyperbola is x²/a² + y²/b² = 1
3) the equation of the hyperbola is x²/a² - y²/b² = -1
4) the equation of the hyperbola is x²/a² + y²/b² = -1