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Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?

a) (x-3)^2 = 20(y-1)
b) (y-1)^2 = 20(x-3)
c) (y-1)^2 = -20(x-3)
d) (x-3)^2 = 20(y-1)

Respuesta :

caylus
Hello,

Remenber:
if S=(0,0) y²=2px then F=(p/2,0 and d:x=-p/2


Let's pose
x'=x-3
y'=y-1 axes passing by the point (3,0) in base (x,y) and (0,0) in base (x',y')

y'²=2p'x'
d': x'=-5=-p'/2 ==> p'=10 and y²=20x'
Returning in base (x,y) : (y-1)²=20(x-3)

Answer B

Answer with Step-by-step explanation:

We have to find:

the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2

General form of Parabola that opens left or right:

(y−k)²=4p(x−h)

Vertex =(h,k)  

Directrix: x=h−p

Here, h=3,k=1 and h-p=-2  i.e. p=h+2=5

Hence, equation of parabola in this case equals

  (y-1)²=4×5(x-3)

i.e. (y-1)²=20(x-3)

Hence, correct option is:

b)  (y-1)²=20(x-3)

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