Answer:
Option C: x = (1/36)*y^2
Step-by-step explanation:
A horizontal parabola is written as
x = f(y) = a*y^2 + b*y + c
If a is positive, the parabola opens to the right.
if a is negative, the parabola opens to the left.
And the vertex of the parabola has the y-value:
y = -b/2a
and the x value
x = f(-b/2a)
For our parabola, we know that:
Opens to the right:
Then the only options left are:
C) x = (1/36)*y^2
D) x = (1/6)*y^2
Because in both cases b = 0, both of the equations have the vertex in the point (0, 0).
Now let's see wich one has a focus at (9, 0)
If the vertex of our equation is:
(h, k)
Then the focus will be:
(h + a, k)
Where a is the directrix of the equation.
Here we know that the vertex is (0, 0) and the focus is (9, 0)
Then:
(0 + a, 0) = (9, 0)
The directrix is 9.
And the directrix is such that:
(x - h)^2 = 4*a*(y - k)
Replacing the values of h and k (both are zero) we get:
x^2 = 4*a*y
And we know that: a = 9
x^2 = 4*9*y
x^2 = 36*y
if we isolate y, we get:
(1/36)*x^2 = y
This is option C.
Then the correct option is C.
