# How do you find the focus of the parabola with directrix y=1 and vertex (1,2)?

Aug 25, 2017

$\text{focus at } \left(1 , 3\right)$

#### Explanation:

$\text{the focus is the same distance from the vertex as the}$
$\text{directrix is from the vertex but on the other side}$
$\text{from the directrix}$

$\text{the distance p from the directrix } = 2 - 1 = 1$

$\Rightarrow \text{focus at } \left(1 , 2 + p\right) = \left(1 , 2 + 1\right) = \left(1 , 3\right)$