Need help writing equation of parabola?

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Vertex (7, 5):

h = 7
k = 5

Directrix:

x = 1

Since the directrix is to the left of the vertex, the parabola will be horizontally-oriented and opening to the right.

p = h - x:

p = 7 - 1
p = 6

a = 1 / 4p:

a = 1 / 4(6)
a = 1/24

Equation:

x = a(y - k)² + h:

x = 1/24 (y - 5)² + 7
x = 1/24 (y² - 10y + 25) + 7
x = 1/24 y² - 5/12 y + 25/24 + 7
x = 1/24 y² - 5/12 y + 25/24 + 168/24
x = 1/24 y² - 5/12 y + 193/24
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or

x = 0.0417y² - 0.4167y + 8.0417
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 ...Show more

Standard equation:

y= a(x-h)^2 + k {(h,k) is the vertex}

Re-written as:

(x – 7)^2 = 4p(y – 5) {4p = 1/a}

Assuming Directrix Y=1,

Distance between vertex and directrix = absolute value (1-5) = +4 = p

(x-7)^2 = 4(4)(y-5)
y-5 = [(x-6)^2]/16
y= [(x-6)^2]/16 + 5...Show more

Directrix cannot = 1
It can be x = 1 or y = 1...Show more

Y = x^2 - 6x - 1 ==> y = (x^2 - 6x + 9) - 1 - 9 ==> y = (x - 3)^2 - 10 EDIT: relying on the learn, the typical types of parabolas do differ. In this case, the reply is A. Hope this helps!...Show more

(x-7)^2 +(y-5)^2 =(x-1)^2
x^2-14x +49 +y^2-10y +25 =x^2-2x+1
y^2-10y +25 =12x-48
(y-5)^2 =12x-48
12x =(y-5)^2+48
x = (1/12)(y-5)^2 +4 ...............Ans...Show more