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The equations of the pairs of opposite sides of a rectangle are $x^{2} - 7 x + 6 = 0 and y^{2} - 14 y + 40 = 0$ the equation of the diagonal nearer the origin is

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$6 x + 5 y - 56 = 0$

$5 x - 6 y + 14 = 0$

$6 x - 5 y + 14 = 0$

$6 x + 5 y - 14 = 0$

answer is B.

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Detailed Solution

Vertices of the rectangle are $A (1, 4) B (6, 4), C (6, 10)$ and D(1, 10)

Equation of $A C$ is $6 x - 5 y + 14 = 0$

Equation of $B D$ is $6 x + 5 y - 56 = 0$

$A C$ is nearer the origin.

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