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Question

If the curves y=2(xa)2 and y=e2x touches each other, then 'a' is less than

A
-1
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B
\N
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C
1
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D
2
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Solution

The correct option is D 2
If two curves touch each other at a point, then the slope of the two curves at that point is equal.
m1=m2 at P
4(xa)=2e2x
4(xa)=22(xa)2
x=a or x=a+1

If x=a then first curve y = 0
second curve, y=e2a but e2a0 a ϵ R
So xa.
Now if x=a+1
first curve y=2
So (x,y)(a+1,2)
(x, y) lies on second curve 2=e2(a+1)
2a+2=ln 2
a=12(ln 22)
1<a<0

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