# The equations of a pair of opposite sides of a parallelogram are x^2 - 5x + 6 = 0 and y^2 - 6y + 5 = 0. The equations of its diagonals are

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The equations of a pair of opposite sides of a parallelogram are x2 - 5x + 6 = 0 and y2 - 6y + 5 = 0. The equations of its diagonals are

(a)   x + 4y = 13,y = 4x - 17

(b)  4x + y = 13, = x - 7

(c)  4x  + y = 13, y = 4x - 7

(d)  y - 4x = 13, y + 4x = 7

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Correct option (c)  4x  + y = 13, y = 4x - 7

Explanation :

We have

x2 − 5x + 6 = (x − 2)(x -3)

y2 − 6y + 5 = (y − 1)(y - 5)

Therefore, the sides of the parallelogram are

x = 2, x = 3 and y = 1, y = 5

Therefore, the vertices of the rectangle are A(2, 1), B(3, 1), C(3, 5) and D(2, 5). Hence, the equation of AC is