If a variable line drawn through the intersection of the lines x/3 + y/4 = 1 and x/4 + y/3 = 1, meets the coordinate axes at A and B, (A ≠ B), then the locus of the midpoint of AB is:

(B) 4(x + y)² − 28(x + y) + 49 = 0

(D) 14(x + y)² − 97(x + y) + 168 = 0

Coordinate Geometry: JEE Main 2016 Mathematics question

JEE Main 2016 · 9 Apr, Morning shift · Q5565

JEE Main 20169 Apr, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

If a variable line drawn through the intersection of the lines

{x \over 3} + {y \over 4} = 1

and

{x \over 4} + {y \over 3} = 1,

meets the coordinate axes at A and B, (A

\ne

B), then the locus of the midpoint of AB is :

JEE Main 2016 · 9 Apr, Morning shift · Q5565

JEE Main 20169 Apr, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

If a variable line drawn through the intersection of the lines

{x \over 3} + {y \over 4} = 1

and

{x \over 4} + {y \over 3} = 1,

meets the coordinate axes at A and B, (A

\ne

B), then the locus of the midpoint of AB is :