`x=4y^2` Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

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One of the vertex form of the parabola is,

`(y-k)^2=4p(x-h)`   where (h,k) is the vertex and 

p is the distance between vertex and focus and also the same distance between the vertex and the directrix,

Given equation is `x=4y^2`

Graph of the equation is attached.

Rewrite the equation in the standard...

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One of the vertex form of the parabola is,

`(y-k)^2=4p(x-h)`   where (h,k) is the vertex and 

p is the distance between vertex and focus and also the same distance between the vertex and the directrix,

Given equation is `x=4y^2`

Graph of the equation is attached.

Rewrite the equation in the standard form,

`y^2=1/4x`

`4p=1/4`

`=>p=1/16`

`(y-0)^2=4(1/16)(x-0)`

Vertex is at (h,k) i.e (0,0)

Focus is at (h+p,k) i.e `(1/16,0)`

Axis of symmetry is the horizontal line passing through the vertex, i.e y=0

Directrix being perpendicular to the axis of symmetry is the vertical line,

Directrix is x=h-p

Directrix is x=`0-1/16=-1/16`

 

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