 Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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.
5 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/a
If the line touches the curve,
-b/a = -b/a e^(-x/a)
or x = 0
Hence, proved
Thanks
Bharat Bajaj
IIT Delhi
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
7 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Other Related Questions on Differential Calculus

View all Questions »  Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  Course Features

• 51 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions