Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

a. f(x) = -1/8 (x - 2)2 + 6
b. f(x) = 1/8 (x - 2)2 + 6
c. f(x) = -1/8 (x + 2)2 + 8
d. f(x) = 1/8 (x + 2)2 + 8

x+y = 29, 5x + 2y = 100

step-by-step explanation:

i'm guessing it was a multiple first option was the correct answer

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: