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Question

If the line ax+by+c=0 is a normal to the curve x3y=1, then ab is?

A
Always positive
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B
Always negative
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C
May be positive or negative
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D
Cannot say anything
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Solution

The correct option is B Always negative
convert the equation in the form of y = mxtc
when m is the slope & c is the y interrupt
ax + by + c = 0
ax + by = -c
by = -c - ax
y = axbc
slope of the line is ab
equation of curve is x3y=1
differentiating the equation of cover w r.t x we
have
ddx(x2y)=ddx(1)
x3dydx+3n2y=0
dydx=3x2yx=3yx=3yx =slope of tang
slope of normal will be x3y
Now since the line is normal to curve
x3y=ab [Always -ve]

1187672_1298819_ans_13e6b406d35349dbbe5319ebe4785036.jpg

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