Question

Find the curve which passes through a,1 and has a subtangent of constant length equal to a .

Answer 1

Answer:

ANSWER

y=e

a

x−a

passes through (a,1)

Now

dx

dy

=e

a

x−a

×

a

1

Length of subtangent=

∣

∣

∣

∣

∣

y

dy

dx

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

e

a

x−a

×ae

a

x−a

∣

∣

∣

∣

∣

∣

∣

=∣a∣

=a

Hence required equation is y=e

a

x−a