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Question

If the line ax+by+c=0 is a normal to the curve xy=1. Then

A
a>0,b>0
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B
a>0,b<0
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C
a<0,b>0
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D
a<0,b<0
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Solution

The correct options are
A a>0,b<0
B a<0,b>0
ax+by+c=0
Hence
by=axc
Or
y=abxc
Hence
m=ab
= Slope of normal.
Now
xy+y=0
Or
y=yx
Or
y=1x2
Thus
1y
=x2
Hence
x2=ab
Or
Now x2>0 thus
ab has to be positive.
Hence we are left with 2 options.
Either
a<0 and b>0
Or
a>0 and b<0.

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