I presume you mean the parabola y^2= 4x. A "chord" through (4, 4) is a line through that point and some other point on the parabola. Call two other points \(\displaystyle \left(\frac{y_1^2}{4}, y_1\right)\) and \(\displaystyle \left(\frac{y_2^2}{4}, y_2\right)\). What are the midpoints of the lines through (4, 4) and those two points? What is the slope of a line through those two midpoints? Does that line also pass through (0, 0)?
