What is the focus and the directrix of the graph of x = 1/24y²?

Solution:

Given the focus and the directrix of the graph of x = 1/24y²

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix).

Parabola Standard Equation:

4p(x - h) = (y - k)² is the standard equation for a right-left facing parabola with vertex at (h, k), and a focal length |p|

4⋅6(x - 0) = (y - 0)²

(h, k) = (0, 0) and p = 6

The focus of the parabola is represented by

(h, k + p) and the directrix is y = k - p

Since the parabola is symmetric around the x-axis and so the focus lies a distance p from the center (0,0) along the x-axis.

Hence, focus is:

(0 + p, 0) = (0 + 6, 0) = (6,0)

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance -p from the center (0,0) x-coordinate,

x = 0 - p

x = 0 - 6

x = -6

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What is the focus and the directrix of the graph of x = 1/24y²?

Summary:

The focus and the directrix of the graph of x = 1/24y² are (6, 0) and x = -6.