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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.

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6 years ago bharat bajaj
IIT Delhi
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/aIf the line touches the curve,-b/a = -b/a e^(-x/a)or x = 0Hence, provedThanksBharat Bajajaskiitians facultyIIT Delhi
```
6 years ago
```							The given equation is y = be_x/aPoint where the curve crosses y axis is (0,y)Substituting the point on the curve,  we obtain    y = bSlope of the tangent to the given curve isdy/dx = -b/a e-x/aSlope of tangent at (0,b) is = -b/a Thus, equation of the tangent is(y-b) = -b/a(x-0)i.e. ay - ab = -bxi.e. bx + at = abDividing 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
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one year 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/aIf the line touches the curve, -b/a = -b/a e^(-x/a)or x = 0Thanks and Regards
```
4 months ago
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