The equation of a common tangant to [x^2/a^2] - [y^2/b^2]=1 and [y^2/a^2] - [x^2/b^2]=1 is (1)y=x+{a^2-b^2}^1/2 (2)y=x-{a^2-b^2}^1/2 (3)y=-x+{a^2-b^2}^1/2 (4)y=-x-{a^2-b^2}^1/2

for hyperbola , x²/a² - y²/b² = 1

y intercept of tangent of hyperbola = c = (a²m²- b²)^1/2

for hyperbola , y²/b² - x²/a²

y intersept of tangent of hyperbola = c = (b²m²- a²)^1/2 

for same line , intercept are equal so

a²m²-b² = b²m² - a²

m = -1 so

c =

eq of tangent = y = mx + c

option 3,4 are correct