Find an equation for a Parabola

Question

Find an equation for the parabola that has its vertex at the origin and directrix x=−10. 

If your answer is in the form x^2=Ay, then input here: A= 40y??

if your answer is in the form y^2=Ax, then input here: A= 40

I need help with putting the answer in the form x^2=Ay. The answer 40y is not correct.

Answer 1

y = ax^2 + bx + c

plug in the vertex (0,0), x=0, y=0

0= 0+0+c, c=0

the vertex is midway between focus and directrix, F(0,10)

y = ax^2+ bx+0

y= ax^2+b

plug in another couple points to solve for a and b

such as (20,10) and (-20,10)

10 =a(20^2) + b(20) = 400a+20b

10 =a(-20)^2+ b(-20) = 400a -20b

add

20 = 800a

a= 20/800=1/40

b = 0

y=x^2/40 is the parabola with vertex(0,0) and directrix y=-10

but whoops, you want directrix x=-10

so rotate the parabola 45 degrees clockwise to get

the inverse relation, just switch x and y

x = (y^2)/40

x= .025y^2

or

40x = y^2

the parabola is horizontal, not vertical, so there is no y=ax^2+bx+c to describe it, no matter what the values of a,b orc

Answer 2

Since the directrix is x=-10, then the parabola's axis of symmetry is the x-axis and is opening to the right. The focus is at (10,0) to make the Vertex half way between the directrix and the focus at (0,0). So the parabola is in the form of Ax=y², not y=Ax².