Step 1:

Vertex of the parabola is $\"\"$ and focus is $\"\"$ .

Observe the vertex and focus points, the $\"\"$ coordinates are same and on $\"\"$ axis.

Thus, the parabola is vertical.

Standard form of the parabola with vertex $\"\"$ and focus is $\"\"$ is $\"\"$ .

The directrix is $\"\"$ .

Compare the points with the standard form.

Distance between the vertex and focus is $\"\"$ .

Find the distance between $\"\"$ and .

Distance between the two points $\"\"$ and $\"\"$ is $\"\"$ .

$\"\"$

Substitutue $\"\"$ in the $\"\"$ .

$\"\"$

Standard form of the parabola is $\"\"$ .

Rewrite the equation $\"\"$ .

Thus, option (c) is correct.

Solution:

Standard form of the parabola is $\"\"$ .

Thus, option (c) is correct.