Let the equations of two adjacent sides of a parallelogram ABCD be 2 x-3 y=-23 and 5 x+4 y=23. If the equation of its one diagonal AC is 3 x+7 y=23 and the distance of A from the other diagonal is d, then 50 ~d² is equal to _ _ _ _ _ _.

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 10 Apr, Evening shift · Q47

JEE Main 202310 Apr, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the equations of two adjacent sides of a parallelogram

\mathrm{ABCD}

2 x-3 y=-23

and

5 x+4 y=23

. If the equation of its one diagonal

\mathrm{AC}

3 x+7 y=23

and the distance of A from the other diagonal is

\mathrm{d}

, then

50 \mathrm{~d}^{2}

is equal to ____________.

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