NTA Abhyas JEE Main2020MathematicsStraight LinesPractice
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
Options
- Aa - b 2 a + b a b
- Bb - a a 2 - b 2 a b
- Ca + b a 2 - b 2 a b
- Da - b a 2 + b 2 a b
Correct answer
B. b - a a 2 - b 2 a b
Step-by-step solution
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