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Question

If tangents are drawn to the curve y=x1+x2 such that the tangents are concurrent at (1,12), then

A
Number of such tangents is 3.
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B
Each of the tangents has exactly two points in common with the curve.
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C
Abscissa of point of contact for one of the tangents is 1+2.
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D
Abscissa of point of contact for one of the tangents is 12.
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Solution

The correct options are
A Number of such tangents is 3.
C Abscissa of point of contact for one of the tangents is 1+2.
D Abscissa of point of contact for one of the tangents is 12.
y=x1+x2
dydx=1x2(1+x2)2
Let point of contact be P(a,b).
A(1,12) and b=a1+a2
Then slope of PA= slope of tangent at P
b12a1=1a2(1+a2)2
(a1+a212)(1+a2)2=(a1)(1a2)
(a1)2(a22a1)=0
a22a1=0 or (a1)2=0
a=1±2 or a=1
Thus, there are three possible tangents.

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