Final answer:
To find the focus, directrix, and focal diameter of the parabola x - 7y^2 = 0, rewrite the equation in standard form y^2 = 4px and find p. The focus is at (p, 0), the directrix is the line x = -p, and the focal diameter is 4p. Sketch the graph by drawing the focus, directrix, and symmetrically plotting points on the parabola.
Step-by-step explanation:
To find the focus, directrix, and focal diameter of the parabola, we need to put the equation in the standard form: y^2 = 4px. From the given equation x - 7y^2 = 0, we can rewrite it as y^2 = (1/7)x. Comparing this with the standard form, we can see that p = 1/7. Therefore, the focus is at (p, 0) = (1/7, 0), the directrix is the line x = -p = -1/7, and the focal diameter is 4p = 4(1/7) = 4/7.
Now let's sketch the graph. Since the focus is at (1/7, 0) and the directrix is the line x = -1/7, we can start by drawing a line passing through the focus perpendicular to the directrix. Next, we draw the parabola symmetrically on both sides of the line, using the distance from the focus to a point on the parabola to determine the corresponding x-coordinate. Finally, we can plot a few more points on the parabola to complete the sketch.