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

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vikas askiitian expert · Answer

for hyperbola , x 2 /a 2 - y 2 /b 2 = 1 y intercept of tangent of hyperbola = c = (a 2 m 2 - b 2 ) 1/2 for hyperbola , y 2 /b 2 - x 2 /a 2 y intersept of tangent of hyperbola = c = (b 2 m 2 - a 2 ) 1/2 for same line , intercept are equal so a 2 m 2 -b 2 = b 2 m 2 - a 2 m = -1 so c = eq of tangent = y = mx + c option 3,4 are correct

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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

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

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