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Question

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

The equations to its diagonals are


A

x+4y=13,y=4x-7

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B

4x+y=13,4y=x-7

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C

4x+y=13,y=4x-7

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D

y-4x=13,y+4x=7

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Solution

The correct option is C

4x+y=13,y=4x-7


Step 1: Vertices of a parallelogram.

x2-5x+6=0x-2x-3=0x=2&3

y2-6y+5=0y-1y-5=0y=1&5

So the vertices of the parallelogram are A2,1,B3,1,C3,5&D2,5.

Step 2: Equation of lines AC&BD.

Slope of AC is calculated as

y2-y1x2-x1=5-13-2=4

Equation of ACis calculated as

y-y1=mx-x1y-1=4x-2y-1=4x-8y=4x-7

Slope of BD is calculated as

y2-y1x2-x1=5-12-3=-4

Equation of BDis calculated as

y-y1=mx-x1y-1=-4x-3y-1=-4x+12y+4x=+13

Hence, the equations of the diagonals are 4x+y=13,y=4x-7 and therefore option C is the correct answer.


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