Q. The equation to a pair of opposite sides of a parallelogram are $x^{2} - 5x + 6 = 0$ and $y^{2} - 6y + 5 = 0$, the equation to its diagonals are
A) $x + 4y = 13$ and $y = 4x - 7$
B) $4x + y = 13$ and $4y = x - 7$
C) $4x + y = 13$ and $y = 4x - 7$
D) $y - 4x = 13$ and $y + 4x = 7$
Explanation
(c)
$Equation\ of\ diagonal\ d_{1}\ is\ y - 1 = \frac{5 - 1}{3 - 2}(x - 2)$
$\Rightarrow \ y = 4x - 7$
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$Equation\ of\ diagonal\ d_{2}\ is\ y - 1 = \frac{5 - 2}{2 - 3}(x - 3)$
$\Rightarrow 4x + y = 13$
So, equations are, $4x + y = 13$ and $y = 4x - 7$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.