# Tangent to a curve

#### Bushy

##### Member
Hi there,

The function $f(x)= e^x+k$ has a tangent to the curve at $x=a$ and going through the origin. Find $k$ in terms of $a$

#### Plato

##### Well-known member
MHB Math Helper
The function $f(x)= e^x+k$ has a tangent to the curve at $x=a$ and going through the origin. Find $k$ in terms of $a$
The equation of the tangent line is $y-f(a)=f^{\prime}(a)(x-a)$.
Now let $x=0~\&~y=0$ then solve for $k$.

#### Bushy

##### Member
$y-f(a) = f'(a)(x-a)$

and

$0-(e^a+k) = e^a(0-a)$

so

$k=e^a(a-2)$