The vertex of a parabola is (6,2), and the equation of its directrix is y = 4. What is the equation of this parabola in standard form?

(y−2)2=8(x−6)

(x−6)2=−8(y−2)

(y−2)2=−8(x−6)

(x−6)2=8(y−2)

Step-by-step explanation:

If you plot the vertex and the directrix, you'll see that the directrix is a horizontal line above the vertex. That means that the parabola opens upside down and has the standard equation:

where h and k are the coordinates of the vertex and p is the number of units between the directrix and the vertex. From the vertex we determine that h = 6 and k = 2. And by counting, we determine that p = 2. Filling in the equation then gives us:

and simplifying just a tiny bit will get us what we need:

which is the second choice down.

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