Question

Show that x/a+y/b=1 touches the curve y=b (e)^(x/a) at the point where the curve crosses y-axis

Answer 1

I am guessing that they will TOUCH each other if they both have equal tangents at any point (a,b)

Answer 2

Therefore,tangent of 1st one=>b/a
tangent of 2nd one=>b (e)^(x/a) itself?i am confused do we have to take log or not..
am i going correct?

Answer 3

Hmm, if they "touch", that should mean that they `intersect` at some point, right?

\[\large \frac{x}{a}+\frac{y}{b}=1 \qquad\qquad \rightarrow\qquad\qquad y=b-b\frac{x}{a}\]

Setting them equal to one another,\[\large b-b\frac{x}{a}=b e^{x/a}\]
And then ummm simplifying some stuff down..\[\large 1-\frac{x}{a}=e^{x/a}\]

This only holds true for one particular x value, do you know which one? :D

The tangent line thing is interestinggggg,
I'm not sure where it's leading us though.
Seems to make more sense though, since this is a calculus problem lol.

Answer 4

touching and intersecting are different things.............

Answer 5

Why would they be different..?

Answer 6

if they are TOUCHING..

then the tangent at any point say alpha,beta is same

here tangent at any point alpha,beta is not same