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Question

Equation to a pair of opposite sides of a parallelogram are x25x+6=0 and y26y+5=0.
a and b are respectively the sum of the intercepts made by the diagonals on x-axis and y-axis respectively then a+b=k2+10 then k equals to

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Solution

x25x+6=0
Or x=2,3

y26y+5=0
Or y=1,5

Hence, the vertices of the parallelogram are A(2,1),B(3,1),C(3,5) and D(2,5)

Let BD,AC be the two diagonals
BD=y1x3=41
y1=4x+12
y+4x=13
b1=13,a1=134 [Intercepts on x axis and y axis]

AC=y1x2=4
y=4x8+1
y=4x7

b2=7,a2=74 [Intercepts on x and y axis respectively]

a+b=6+204=k2+10 [a=a1+a2,b=b1+b2]

11=k2+10
k=2

641355_191614_ans_35456aaedb55462a99a24a597dac0f19.png

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