Method of finding cartesian equation of? (1 Viewer)

[fabl]

what is the Method of finding cartesian equation of this conic parabola.
How do we find the vertex or the focal length?

Given: focus at (-4,0) and directrix at -1

 

[seventhroot]

get the focal length and then sub that into x^2 = 4ay

2ez 4 square

 

[braintic]

what is the Method of finding cartesian equation of this conic parabola.

Given: focus at (-4,0) and directrix at -1

For starters, this is a 2 unit question.

Secondly, what is the EQUATION of the directrix? Is it x=-1 or y=-1 ?

It can't be done without knowing that.

 

[fabl]

For starters, this is a 2 unit question.

Secondly, what is the EQUATION of the directrix? Is it x=-1 or y=-1 ?

It can't be done without knowing that.

Sorry about that, the directrix is x= -1

 

[fabl]

get the focal length and then sub that into x^2 = 4ay

2ez 4 square

How do we find the focal length between the focus point and the directrix from vertex?

 

[braintic]

Halfway between (-4,0) and x=-1 is (-5/2, 0) - that is the vertex.
Since the focus is to the left of the vertex, the parabola is concave left.
Distance from (-4,0) to (-5/2, 0) is -5/2 - (-4) = 3/2 - that is the focal length a.
Subbing into y^2 =-4ax:
y^2 = -6(x+5/2)
or y^2 = -3(2x+5)