# How do you find the vertex, focus and directrix of #4x-y^2-2y-33=0#?

##### 1 Answer

Please see the explanation.

#### Explanation:

Given:

Add #y^2 + 2y + 33 to both sides:

Divide both side by 4:

This type of parabola opens to left or right. Because the coefficient, a, of the

The vertex form of an equation of this type of parabola is:

where "a" is the coefficient of the

The focus of this type is located at

The equation of the directrix is

Lets put equation [1] in vertex from. Add zero to equation [1] in the form of

Factor

Please observe that the right side of the pattern

Substitute the left side of the pattern into the ()s in equation [2]:

Substitute -1 for every k:

Simplify the constant term:

The vertex is at

The focus is at

#(8 + 1/(4(1/4)), -1)

This simplifies to:

(9, - 1)#

The equation of the directrix is