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The focus of a parabola is (3,−7) and the directrix is y=−4.

 

What is an equation of the parabola?

A. (x−3)2=−1.5(y+5.5)

B.(x−3)2=−12(y+10)

C.(x−3)2=−3(y+10)

D.(x−3)2=−6(y+5.5)

 May 23, 2018
 #1
avatar+99604 
+2

The focus is above the directrix....so this parabola turns downward

 

The vertex  is given as  ( 3, (-7 + -4) / 2  )   =  (3, -5.5  )

 

And we have this equation

 

( x - h)^2   = 4p ( y - k)  where  the  vertex   is  ( h, k)   and p  is the (negative) distance between  the focus and the vertex and is given by: 

 

p  = ( -7 - - 5.5)  

 

p = (-7 + 5.5)

 

p = -1.5

 

So...the equation is :

 

( x - 3)^2   =  4(-1.5) ( y + 5.5)

 

(x - 3)^2  = -6(y + 5.5)   ⇒    Answer "D"

 

 

cool cool cool

 May 23, 2018

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