The equations to a pair of opposite sides of a parallelogram are $x^{2} - 5 x + 6 = 0 a n d y^{2} - 6 y + 5 = 0$ the equation of a diagonal can be

x + 4 y = 13

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4 x + y = 13

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y = 4 x - 7

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y = 4 x + 7

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Solution

The correct options are
A $y = 4 x - 7$
C $4 x + y = 13$

$x^{2} - 5 x + 6 = 0$
$\Rightarrow (x - 3) (x - 2) = 0$
$\Rightarrow x = 2, x = 3$
and $y^{2} - 6 y + 5 = 0$
$\Rightarrow y = 1, y = 5$
Vertices of the parallelogram are
$A (2, 1), B (3, 1),$ $C (3, 5), D (2, 5)$
equation of $A C$ is
$y - 1 = \frac{5 - 1}{3 - 2} (x - 2)$

$\Rightarrow y = 4 x - 7$
equation of $B D$ is
$y - 1 = \frac{5 - 1}{3 - 2} (x - 3)$

$\Rightarrow 4 x + y = 13$

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The equations to a pair of opposite sides of a parallelogram are x2−5x+6=0 and y2−6y+5=0 the equation of a diagonal can be

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The equations to a pair of opposite sides of a parallelogram are $x^{2} - 5 x + 6 = 0 a n d y^{2} - 6 y + 5 = 0$ the equation of a diagonal can be