Differential Calculus> Show that the line x/a + y/b =1 touches t...

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.

Faiz , 10 Years ago

Grade 12

3 Answers

bharat bajaj

Last Activity: 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

Approved

Chaitanya

Last Activity: 6 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

Last Activity: 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