Solve the Problem $3.8$ Meters in Diameter, That Collects Light from Space

Solve the problem.
-The quality of the images from an orbital telescope result from a large parabolic mirror, $3.8$ meters in diameter, that collects light from space.

Suppose that a coordinate system is chosen so that the vertex of a cross section through the center of is located at $( 0,0 )$ . Furthermore, the focal length of the mirror is $56.8 \mathrm {~m}$ . Assume that $x$ and $y$ are in meters. Write an equation of the parabolic cross section of the mirror for $- 1.9 \leq x \leq 1.9$ .

A) $x ^ { 2 } = 113.6 y$ for $- 1.9 \leq x \leq 1.9$
B) $x ^ { 2 } = 56.8 y$ for $- 1.9 \leq x \leq 1.9$
C) $y ^ { 2 } = 227.2 x$ for $- 1.9 \leq y \leq 1.9$
D) $x ^ { 2 } = 227.2 y$ for $- 1.9 \leq x \leq 1.9$