The sum of the intercepts on the coordinate axes made by a line passing through the point a , b and the common point of x a + y b = 1 and x b + y a = 1 is

Question

The sum of the intercepts on the coordinate axes made by a line passing through the point a , b and the common point of x a + y b = 1 and x b + y a = 1 is, a - b 2 a + b a b, b - a a 2 - b 2 a b, a + b a 2 - b 2 a b, a - b a 2 + b 2 a b

MARKS App · Accepted Answer

Point of intersection of x a + y b = 1 and x b + y a = 1 is a b a + b , a b a + b Now, line joining a , b and a b a + b , a b a + b is y - b x - a = a b a + b - b a b a + b - a ⇒ y - b a 2 = b 2 x - a ⇒ x a b - a b + y b a - b a = 1 ⇒ sum of the x intercept and the y intercept is equal to a b - a b + b a - b a = b - a a 2 - b 2 a b

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