Question

Find the vertex, focus, directrix, and focal width of the parabola.

(y + 2)^{2 = -8(x - 1)}

Answer 1

Vertex

Parabolas always have a lowest point ( or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the vertex.

Focus and Directrix

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix.

Focal width

The focal width can be defined simply as the distance between the two arms of the parabola .

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Now let's look at the vertex forms of a parabola :

we are given a parabola :

which is of the form : that is  

here  

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So now the vertex is ( h , k ) = ( 1 , -2 )

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directrix is    that is

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focus is   that is    that is  

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So the focal width of the parabola is