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Question

If x2+αy2+2βy=a2 represent a pair of perpendicular lines, then β =

A
4a
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B
a
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C
2a
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D
3a
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Solution

The correct option is B a
x2+αy2+2βy=a2
Adding and subtracting β2αfrom the above equation,
x2+αy2+2βy+β2αβ2αa2=0
x2+(αy+βα)2=a2+β2α
For pair of straight lines ax2+by2+2hxy+2gx+2fy+c=0,
the condition of perpendicularity |a+b|=0 can be applied.
1+α=0 or α=1
also line satisfies
abc+2hgfaf2ch2bg2=0
so, a2β2=0
β=a.

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