A) Is \[ey+x=2\]
B) Is \[x+y=e\]
C) Is \[ex+y=1\]
D) Does not exist
Correct Answer: A
Solution :
[a] The point of intersection is \[\left( 1,\text{ }{{e}^{-1}} \right)\] \[\because \,x=1\], so equation of the curve is \[y={{e}^{-x}}\] \[\Rightarrow \frac{dy}{dx}=-{{e}^{-x}}\] \[{{\left[ \frac{dy}{dx} \right]}_{x=1}}=-{{e}^{-1}}\]. Hence equation of tangent is \[y-{{e}^{-1}}=-{{e}^{-1}}\left( x-1 \right)\text{ }or,\text{ }ey+x=2.\]
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