Focus and Directrix of the Parabola:
The focus of the parabola is given as (1,2) and the directrix as 2x + 3y + 1 = 0.

Equation of the Tangent at the Vertex:
To find the equation of the tangent at the vertex of the parabola, we first need to determine the vertex of the parabola. The vertex can be calculated as the midpoint of the focus and the point of intersection of the directrix and the line passing through the focus and perpendicular to the directrix.
1. Find the midpoint of the focus and the point of intersection of the directrix:
- The vertex lies on the line perpendicular to the directrix passing through the focus.
- The slope of the line passing through the focus is -3/2 (opposite reciprocal of the directrix).
- Using the midpoint formula, we can find the vertex as (h, k).
2. Determine the equation of the tangent at the vertex:
- The tangent at the vertex is a horizontal line passing through the vertex.
- Since the parabola is symmetric about its axis, the tangent will be parallel to the directrix.
- The equation of the tangent will be of the form y = k, where k is the y-coordinate of the vertex.
Therefore, the equation of the tangent at the vertex of the parabola is y = k, where k is the y-coordinate of the vertex.

Ans is 4x-6y+5=0