JEE MATHEMATICS MCQ: STRAIGHT LINES

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Analyzing +4 | -1

A variable straight line drawn through the point of intersection of lines

\frac{x}{a}+\frac{y}{b}=1

and

\frac{x}{b}+\frac{y}{a}=1

, meets the coordinate axes in

A

and

B

. Then, the locus of the mid-point of

A B

View answer and explanation

Correct option: D

2 x y(a+b)=a b(x+y)

Option D (

2 x y(a+b)=a b(x+y)

) is correct because it represents the locus of the midpoint of AB, derived from the intersection of the given lines and the variable line.

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\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0