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Grade: 12
        
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.
6 years ago

Answers : (3)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							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
6 years ago
Chaitanya
13 Points
							
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
one year ago
Rishi Sharma
askIITians Faculty
454 Points
							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
14 days ago
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