Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7. a. f(x) = −one twenty-fourth (x − 1)2 − 5 b. f(x) = one twenty-fourth (x − 1)2 − 5 c. f(x) = −one twenty-fourth (x + 5)2 + 1 d. f(x) = one twenty-fourth (x + 5)2 + 1

First find the distance between the focus and the point (x, y)

distance = sqrt ( (x + 5}^2 + (y + 5)^2)

distance between the directrix and (x, y) is

|y - 7|

These distances are equal  so , squaring we have:-

(x + 5)^2 + (y + 5)^2 = (y - 7)^2

x^2 + 10x + 25 + y^2 + 10y + 25 =  y^2 - 14y + 49

24y =  -x^2 - 10x - 1

24y =  - (x^2 + 10x) - 1

24y = - [(x + 5)^2 - 25] - 1

24y = -(x + 5)^2  + 24

y = -(1/24)(x + 5)^2 + 1       (answer)

Option C

it’s the first one your welcome

i get you, what you should do is think of the positive things that would come out of it. it will make yours parents proud and raise your grade. you should always try and if you can't focus tell the teacher.