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Question

The abscissa of a point on the curve xy=(a+x)2, at which the normal cuts off numerically equal intercepts from the coordinate axes is

A
a2
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B
2 a
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C
a2
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D
2 a
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Solution

The correct option is C a2

xy=(a+x)2
y+xy=2(a+x)
Now, y=±1
y±x=2(a+x)
(a+x)2x±x=2(a+x)
±x=2(a+x)(a+x)2x
±x2=(a+x)(xa)
±x2=x2a2
2x2=a2
x=±a2

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