Question 265122
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The parabola {{{x^2=4py}}} has vertex (0,0), focus (0,p), 

equation of directrix y=-p,

equation of axis of symmetry x=0 (the y-axis)

1.) {{{y=(1/28)x^2}}}

Multiply through by 28

{{{28y=x^2}}}

Turn backwards:

{{{x^2=28y}}}

so comparing to 

{{{x^2=4py}}}

{{{4p=28}}}
{{{p=7}}}

So it has vertex (0,0), focus (0,p) = (0,7), 

equation of directrix y=-p, or y=-7

equation of axis of symmetry x=0 (the y-axis)

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The parabola {{{y^2=4px}}} has vertex (0,0), focus (0,p), 

equation of directrix x=-p,

equation of axis of symmetry y=0 (the x-axis)


2.) {{{x=(1/8)y^2}}}

Multiply through by 8

{{{8x=y^2}}}

Turn backwards:

{{{y^2=8x}}}

Compare to 

{{{y^2=4px}}}

{{{4p=8}}}
{{{p=2}}}

So it has vertex (0,0), focus (p,0) = (2,0), 

equation of directrix x=-p, or x=-2

equation of axis of symmetry y=0 (the x-axis)

Edwin</pre>