Question

Find the equation for the parabola that has its vertex at the origin and has directrix at x=1/48

Answer 1

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is $x= \frac{1}{12}\cdot y^{2}$.

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

$x - h = 4\cdot p \cdot (y-k)^{2}$

Where:

$h$, $k$ - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

$p$ - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

$p = x_{D} - x_{V}$

$p = \frac{1}{48}-0$

$p = \frac{1}{48}$

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is $x= \frac{1}{12}\cdot y^{2}$.