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Smoores Smoores
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12 years ago
Please explain your answer in detail.

Q1: Find, in cartesian form, an equation of the parabola whose focus and directrix
(1,1), y+1=0

Q2: find the coordinates of the focus and an equation of hte directrix of the parabola with equation
y^2=4x+4
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tony51092tony51092
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12 years ago
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12 years ago
believe it or not I have seen different formulas in different books so it may be hard sto explain

I like the one:    y=  4p(x-h)^2 +k      or     x= 4p(y-k)^2 + h

the vertex will be 1/2 way between the focus and directrix
since the dir is a y equation you should know that the parab opens up/down not right/left so the x value of the vertex is the x value of the focus or  1
since the dir is y= -1  (if you solve for y)then you know the y value is between 1 and -1  at 0       (1 + -1)/2

with vertex (1,0)  h=1 k=0  

The distance from focus to vertex determines p in this case p=1

then plug in the #'s
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