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Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1

 Feb 24, 2020

Best Answer 

 #1
avatar+349 
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The parabola is the set of all points (x,y) that are equidistant from the focus and directrix.

 

So, using the distance formula, we have:

 

√[(x+5)2 + (y-5)2] = √[(x-x)2 + (y+1)2]

 

x2 + 10x + 25 + y2 - 10y + 25 = y2 + 2y + 1

 

x2 + 10x + 25 = 12y - 24

 

(x + 5)2 = 12(y - 2)

 

y - 2 = (1/12)(x + 5)2

 

y = (1/12)(x + 5)2 + 2

 Feb 24, 2020
 #1
avatar+349 
+1
Best Answer

The parabola is the set of all points (x,y) that are equidistant from the focus and directrix.

 

So, using the distance formula, we have:

 

√[(x+5)2 + (y-5)2] = √[(x-x)2 + (y+1)2]

 

x2 + 10x + 25 + y2 - 10y + 25 = y2 + 2y + 1

 

x2 + 10x + 25 = 12y - 24

 

(x + 5)2 = 12(y - 2)

 

y - 2 = (1/12)(x + 5)2

 

y = (1/12)(x + 5)2 + 2

TacoBell Feb 24, 2020

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