NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

If the point M h , k lie on the line 2 x + 3 y = 5 such that M A - M B is maximum where A 1 , 2 and B 2 , 3 , then the value of h + k is

Correct answer

1.8

Step-by-step solution

As, M A - M B ≤ A B ∴ M A - M B m a x i m u m = A B , which is possible when M is the point of intersection of the line joining A 1 , 2 ,   B 2 , 3 and 2 x + 3 y = 5 . Equation of the line joining A   &   B is x - y + 1 = 0 Hence, the point of intersection is h = 2 5 ,   k = 7 5 Hence, h + k = 9 5 = 1 . 8

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