What is the equation in standard form of the parabola with a focus at (42,-31) and a directrix of y= 2?
Please observe that the directrix is a horizontal line
Therefore, the parabola is the type that opens upward or downward; the vertex form of the equation for this type is:
The x coordinate of the vertex is the same as the x coordinate of the focus:
The y coordinate of the vertex is halfway between the directrix and the focus:
The equation to find the value of
Simplify the fraction:
Expand the square:
Distribute the fraction:
Combine like terms:
We will solve this Problem using the following Focus-Directrix
Property (FDP) of the Parabola.
FDP : Any point on a Parabola is equidistant from the
Focus and the Directrix.
Let, the point
the Focus and the Directrix of the Parabola, say S.
Then, using the Distance Formula, we have, the distance,
Knowing that the
as Respected Douglas K. Sir has already derived!