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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
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
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