# How do you identify the vertex, focus, directrix and the length of the latus rectum and graph #4(x-2)=(y+3)^2#?

##### 1 Answer

Please see the explanation.

#### Explanation:

Rewrite the equation in the vertex form

where

Divide by both sides by 4:

Write the + as a - -

Add 2 to both sides:

Now, that the equation is in standard form, please observe that the vertex is at

The distance, in the x direction, from the vertex from to the focus is:

Therefore, we add 1 to the x coordinate of the vertex and we see that the focus is

The directrix is the vertical line the same distance in the opposite direction from the vertex so we subtract 1 from the x coordinate of the vertex; making its equation:

Modifying the equation,