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Show that the line x/a + y/b =1 touches the curve y=b e^-x/a at the point where the curve cuts the y axis.

Show that the line x/a + y/b =1 touches the curve y=b e^-x/a at the point where the curve cuts the y axis.

Grade:12

3 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 years ago
The slope of tangent at any point (x,y) for the curve is :
dy/dx = -b/a e^(-x/a)
The slope of line : -b/a
If the line touches the curve,
-b/a = -b/a e^(-x/a)
or x = 0
Hence, proved
Thanks
Bharat Bajaj
askiitians faculty
IIT Delhi
Chaitanya
13 Points
5 years ago
The given equation is y = be_x/a
Point where the curve crosses y axis is (0,y)
Substituting the point on the curve,  we obtain 
   y = b
Slope of the tangent to the given curve is
dy/dx = -b/a e-x/a
Slope of tangent at (0,b) is = -b/a
 
Thus, equation of the tangent is
(y-b) = -b/a(x-0)
i.e. ay - ab = -bx
i.e. bx + at = ab
Dividing the equation by ab,
 x/a + y/b = 1
 
Hence the line touches the curve at the point where the curve crosses y axis 
 
Hence proved
Rishi Sharma
askIITians Faculty 646 Points
4 years ago
Dear Student,
Please find below the solution to your problem.

The slope of tangent at any point (x,y) for the curve is :
dy/dx = -b/a e^(-x/a)
The slope of line : -b/a
If the line touches the curve, -b/a = -b/a e^(-x/a)
or x = 0

Thanks and Regards

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