A) \[ax+by=1\]
B) \[\frac{x}{a}-\frac{y}{b}=1\]
C) \[\frac{x}{a}+\frac{y}{b}=1\]
D) \[ax-by=1\]
Correct Answer: C
Solution :
The curve crosses the y-axis where \[x=0\] \[\therefore \] when \[x=0,\,y=b.\]Hence the point is\[(0,b)\] Now \[\frac{dy}{dx}=-\frac{b}{a}{{e}^{-x/a}}\] \[\therefore \]\[\frac{dy}{dx}=-\frac{b}{a}\] The equation of tangent at \[(0,b)\]is \[y-b=-\frac{b}{a}(x-0)\Rightarrow ay-ab=-bx\] \[bx+ay=ab\] \[\Rightarrow \,\frac{x}{a}+\frac{y}{b}=1\]
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