Introduction:
The equation of the parabola is given as x^2 = 4y, and we need to find the equation of all possible normals to the parabola that are drawn from the point (1,2).

Step 1: Find the slope of the tangent at any point on the parabola:
To find the equation of the normal, we first need to find the slope of the tangent at any point on the parabola. The slope of the tangent at a point (x1, y1) on the parabola is given by the derivative of the equation of the parabola at that point.

Differentiating the equation x^2 = 4y with respect to x, we get:
2x = 4(dy/dx)
Simplifying, we find:
dy/dx = x/2

Step 2: Find the slope of the normal:
The slope of the normal is the negative reciprocal of the slope of the tangent. Therefore, the slope of the normal is given by:
m_normal = -2/x

Step 3: Find the equation of the normal:
We have the slope of the normal (m_normal) and a point on the normal (1,2). Using the point-slope form of a line, we can find the equation of the normal.

The point-slope form of a line is given by:
y - y1 = m(x - x1)

Substituting the values into the equation, we get:
y - 2 = (-2/x)(x - 1)

Simplifying, we find:
y = -2x + 4 + 2/x

Therefore, the equation of the normal to the parabola x^2 = 4y, drawn from the point (1,2), is:
y = -2x + 4 + 2/x

Conclusion:
In conclusion, the equation of all possible normals to the parabola x^2 = 4y, drawn from the point (1,2), is given by y = -2x + 4 + 2/x. This equation represents a family of lines that are perpendicular to the tangent at different points on the parabola and pass through the point (1,2).