Introduction:
The given problem involves finding the area of a triangle formed by the tangents and the chord of contact from a point (x1, y1) to the parabola y^2 = 4ax.

Step 1: Find the coordinates of the point of contact:
To find the point of contact, substitute y = y1 in the equation of the parabola and solve for x.
y^2 = 4ax
y1^2 = 4ax1
x1 = y1^2 / 4a
Therefore, the coordinates of the point of contact are (x1, y1).

Step 2: Find the slope of the tangent:
The slope of the tangent can be found by differentiating the equation of the parabola with respect to x and substituting the x-coordinate of the point of contact.
Differentiating y^2 = 4ax with respect to x:
2y(dy/dx) = 4a
dy/dx = 2a/y1

Step 3: Find the equation of the tangent:
Using the point-slope form of a line, the equation of the tangent can be written as:
y - y1 = m(x - x1)
Substituting the values of x1, y1, and m:
y - y1 = (2a/y1)(x - x1)

Step 4: Find the points of intersection:
To find the points of intersection of the tangents, we need to solve the equation of the tangents simultaneously. Let's assume the equation of the tangents as:
y - y1 = (2a/y1)(x - x1) ... (1)
y - y1 = (2a/y1)(x - x1) ... (2)

Step 5: Find the equation of the chord of contact:
The chord of contact is the line joining the points of intersection of the tangents to the parabola. We need to find the equation of this chord. Let's assume the equation of the chord of contact as:
y - y1 = mx - x1 ... (3)

Step 6: Find the coordinates of the points of intersection:
We can solve equations (1), (2), and (3) simultaneously to find the coordinates of the points of intersection.

Step 7: Calculate the area of the triangle:
Once we have the coordinates of the points of intersection, we can calculate the length of the base (the chord of contact) and the height (the perpendicular distance between the chord of contact and the point of contact). The area of the triangle can then be calculated using the formula: Area = (1/2) * base * height.

Conclusion:
By following the steps outlined above, we can find the area of the triangle formed by the tangents and the chord of contact from a given point to the parabola y^2 = 4ax.