Write the equation of the problems that has a focus at (7,3) and directrix of x=-3

Answer 1

The equation of a parabola with a focus (a,b) and a directrix equation x or y = c can be modeled by the below equation:

(x-a)^2 + (y-b)^2 = (x-c)^2

Substituting our known information into the problem:

(x-7)^2 + (y-3)^2 = (x+3)^2 ---> Leave the y-bubble alone, since it is the only bubble with a y-component.

Expanding:

x^2 -14x + 49 + (y-3)^2 = x^2 + 6x + 9 ----> Combining like terms and solving for x:

-14x + 49 + (y-3)^2 = 6x + 9

(y-3)^2 + 40 = 20x

[(y-3)^2]/20 + 2 = x

Parabola Equation: x = (1/20)(y-3)^2 + 2