Question

Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.

Answer 1

@aum please help

Answer 2

@dumbcow @Hero

Answer 3

a min...

Answer 4

y= a(x-h)2+k

plug in values...

Answer 5

Let (x,y) be any point on the parabola.
The property of a parabola is that any point on the parabola is equidistant from the focus and the directrix. It means, distance of point (x,y) from (7,0) = distance of point (x,y) from the directrix which here is a vertical line x = -7. You can square both sides and equate the square of the distances.
Square of the distance (x,y) from (7,0) = (x-7)^2 + (y-0)^2
Square of the distance (x,y) from x = -7 is: (x + 7)^2
Equate the two:
(x-7)^2 + y^2 = (x+7)^2
y^2 = (x+7)^2 - (x-7)^2
y^2 = (x+7+x-7)(x+7-x+7)
y^2 = (2x)(14)
y^2 = 28x

Answer 6

i thought it was x=1/28y^2

Answer 7

because y^2=28x isnt one of my answer choices