帮我讲一下这个题。---**Extraction Content:** **Question 2:** [湖北七市州 2024 调研] 如图, O 为坐标原点, F 为抛物线 $y^2=2x$ 的焦点, 过点 F 的直线交抛物线于 A, B 两点, 直线 AO 交抛物线的准线于点 D, 设抛物线在点 B 处的切线为 l. (1) 若直线 l 与 y 轴的交点为 E, 求证: $|DE|=|EF|$; (2) 过点 B 作 l 的垂线与直线 AO 交于点 G, 求证: $|AD|^2=|AO| \cdot |AG|$. **Chart Description:** * **Type:** Coordinate plane with a parabola and several lines and points. * **Coordinate Axes:** X-axis labeled 'x' and Y-axis labeled 'y'. The origin is labeled 'O'. * **Parabola:** A curve symmetric about the x-axis, opening to the right. Its vertex is at the origin O. * **Points:** * O: Origin (0,0). * F: A point on the positive x-axis, inside the parabola, labeled 'F'. This is the focus. * A, B: Two points on the parabola. A is in the first quadrant, B is in the fourth quadrant. These points lie on a line passing through F. * D: A point on the directrix of the parabola and also on the line AO. The directrix appears to be a vertical line to the left of the y-axis. D is in the third quadrant. * **Lines:** * Line passing through F, A, and B: A straight line intersecting the parabola at A and B. * Line AO: A straight line passing through the origin O and point A. This line also passes through point D. * Directrix: A vertical line to the left of the y-axis, passing through point D. (Implicitly, it's the directrix of the parabola). * Line l: A line tangent to the parabola at point B. * **Other Elements:** The labels A, B, D, E, F, O, x, y are clearly marked. The parabola equation $y^2=2x$ implies the focus F is at $(p/2, 0)$ where $2p=2$, so $p=1$, and F is at $(1/2, 0)$. The directrix is the line $x = -p/2 = -1/2$. Point D is on this directrix and the line AO. Point E is the intersection of the tangent line l at B and the y-axis. Point G is the intersection of the line perpendicular to l passing through B and the line AO.