The endpoints of two normal chords of a parabola are concyclic. Then the tangents at the feet of the normals will intersect at
a. Tangent at vertex of the parabola
b. Axis of the parabola
c. Directrix of the parabola
d. None of these

Options

A. tangent at vertex of the parabola
B. axis of the parabola
C. directrix of the parabola
D. none of these

Explanation

To solve the problem, we need to analyze the conditions given and use properties of the parabola and the concept of concyclic points.

### Step-by-Step Solution:

1. **Understanding the Parabola**:
We start with the parabola given by the equation \( y^2 = 4ex \). This is a standard form of a parabola that opens to the right.

**Hint**: Recall that the general form of a parabola is \( y^2 = 4px \), where \( p \) is the distance from the vertex to the focus.

2. **Identifying the Points**:
Let the points on the parabola be \( T_1 \) and \( T_3 \) with their respective parameters \( t_1 \) and \( t_3 \). The endpoints of the normal chords are \( T_2 \) and \( T_4 \), which are the points where the normals at \( T_1 \) and \( T_3 \) intersect the parabola again.

**Hint**: The coordinates of points on the parabola can be expressed in terms of their parameters.

3. **Finding the Coordinates of Points**:
The coordinates of the points can be expressed as:
- \( T_1(t_1) = (e t_1^2, 2e t_1) \)
- \( T_3(t_3) = (e t_3^2, 2e t_3) \)

The normals at these points will intersect the parabola again at points \( T_2 \) and \( T_4 \).

4. **Using the Concyclic Condition**:
Since \( T_1, T_2, T_3, T_4 \) are concyclic, we can use the property that the sum of the parameters of these points must equal zero:
\[ t_1 + t_2 + t_3 + t_4 = 0 \]

**Hint**: Remember that if four points are concyclic, the sum of the angles subtended by these points at any point on the circumference is constant.

5. **Finding Relationships**:
From the properties of the normals, we can derive:
\[ t_2 = -t_1 - \frac{2}{t_1}, \quad t_4 = -t_3 - \frac{2}{t_3} \]

**Hint**: The normal at a point on a parabola can be derived from the derivative of the parabola's equation.

6. **Summing the Parameters**:
We can sum the equations:
\[ t_1 + t_2 + t_3 + t_4 = 0 \implies t_1 + (-t_1 - \frac{2}{t_1}) + t_3 + (-t_3 - \frac{2}{t_3}) = 0 \]
This simplifies to:
\[ -\frac{2}{t_1} - \frac{2}{t_3} = 0 \implies t_1 + t_3 = 0 \]

**Hint**: This means that \( t_3 = -t_1 \).

7. **Finding the Intersection of Tangents**:
The equations of the tangents at points \( T_2 \) and \( T_4 \) can be derived. The intersection point of these tangents will be:
\[ Y = A(t_2 + t_4) = 0 \]
Since \( t_2 + t_4 = 0 \).

**Hint**: The tangents at points on the parabola can be expressed in terms of their parameters.

8. **Conclusion**:
The intersection of the tangents occurs at the x-axis, which is the axis of the parabola.

**Final Answer**: The tangents at the feet of the normals will intersect at the axis of the parabola.

### Final Answer:
**b. Axis of the parabola**