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Help 5,6

NotSoSmart  Mar 21, 2018
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5.  If the directrix  is  above the vertex, as in this case,  this parabola turns downward

 

So.....p  = the distance from the directrix to the vertex  = 5

 

So....we have the form

 

-4py  = x^2

-4(5)y = x^2

-20y  = x^2      divide both sides by -20

 

y  = (-1/20)x^2

 

 

6)  First.. in the form  x  = ay^2  ...the vertex is at the origin

 

x = (1/24)y^2    multiply both sides by 24

24x = y^2

 

We have the form

 

4px  = y^2         so   4p  = 24  ⇒   p  = 6

 

This parabola opens to the right  so  the focus  is   (0 + p, 0)  = (0 + 6 , 0 )  = (6, 0)

 

The directrix   is    x =  0 - p   ⇒  x  = 0 - 6  ⇒  x  = -6

 

 

cool cool cool

CPhill  Mar 21, 2018

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