The length of the chord of the parabola $x^2 = 4y$ having equation $x - 2y + 4\sqrt{2} = 0$ is
$6\sqrt{3} \text{ units}$
$8\sqrt{2} \text{ units}$
$2\sqrt{11} \text{ units}$
$3\sqrt{2} \text{ units}$
Step-by-Step Solution
Key Concept: The focus and directrix of a parabola are equidistant from any point on the parabola, and the vertex lies midway between them.
The directrix is given by $x - 2 = 5$ and $y - 4 = 0$, which means $x = 7$ and $y = 4$. However, resolving the intended directrix: if $x - 2 = 5$, then $x = 7$, but this seems inconsistent. Re-interpreting: the directrix is $x = 7$ and the focus coordinate satisfies the parabola property. Given the vertex condition and directrix, the focus is equidistant from the vertex and on the opposite side. Therefore, the required coordinate is $(7, 4)$.
Correct Answer: (7, 4)