The line x a + y b = 1 touches the curve y = b e - x a at the point

Step-by-step solution

Let the point be x 1 ,   y 1 ∴ y 1 = b e - x 1 a ......(i) Also, the slope of the tangent to the curve is d y d x x 1 ,   y 1 = - b a   e - x 1 a   = - y 1 a (by (i)) Now, the equation of tangent of the given curve at point x 1 ,   y 1 is y - y 1 = - y 1 a     x - x 1 ⇒ x a + y y 1 = x 1 a + 1 Comparing with x a + y b = 1 , We get, y 1 = b and 1 + x 1 a = 1 ⇒ x 1 = 0 Hence, the point is ( 0 ,   b ) .