Answered

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What is the equation of the parabola, in vertex form, with focus at (1, -4) and
directrix x= 3?

What Is The Equation Of The Parabola In Vertex Form With Focus At 1 4 And Directrix X 3 class=

Sagot :

sqdancefan

Answer:

  D.  (y +4)² = -4(x -2)

Step-by-step explanation:

The directrix is a vertical line, and the focus is to the left of it. The parabola will open to the left.

The vertex is halfway between the focus and directrix, so is located on the same horizontal line as the focus, at ...

  x = (1 +3)/2 = 2

The focus to vertex distance is the difference in x-coordinates: 1 -2 = -1. This is the value of p in the form ...

  (y -k)² = 4p(x -h) . . . . . . . parabola with vertex (h, k)

The equation is ...

  (y +4)² = -4(x -2)

_____

Additional comment

Once you determine that the directrix is a vertical line, you know the equation will have a y² term. The only answer choice that has that is D.

View image sqdancefan
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