To find the point on the curve y^2 = 4(x-10) nearest to the line x + y = 4, we can follow these steps:

1. Find the equation of the line x + y = 4 in slope-intercept form (y = mx + b):
Rearrange the equation to solve for y:
y = -x + 4

2. Substitute the expression for y in the equation of the line into the equation of the curve:
(-x + 4)^2 = 4(x - 10)

3. Expand and simplify the equation:
x^2 - 8x + 16 = 4x - 40

4. Rearrange the equation to isolate the variable x:
x^2 - 12x + 56 = 0

5. Solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, factoring yields:
(x - 4)(x - 14) = 0

This gives us two possible values for x: x = 4 or x = 14.

6. Substitute these values of x back into the equation of the line to find the corresponding y-values:
For x = 4, y = -4 + 4 = 0
For x = 14, y = -14 + 4 = -10

7. Calculate the distance between each of these points and the line x + y = 4. The distance formula between a point (x1, y1) and a line Ax + By + C = 0 is given by:
d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

For the point (4, 0):
d = |1(4) + 1(0) - 4| / sqrt(1^2 + 1^2) = |0| / sqrt(2) = 0 / sqrt(2) = 0

For the point (14, -10):
d = |1(14) + 1(-10) - 4| / sqrt(1^2 + 1^2) = |14 - 10 - 4| / sqrt(2) = |0| / sqrt(2) = 0 / sqrt(2) = 0

8. As both distances are equal to 0, it means that both points lie on the line x + y = 4 and are equidistant from the line. However, the problem asks for the point on the curve, not the line.

9. Therefore, none of the given options (a), (b), or (c) are correct. The correct answer is "None of these."