Question 1106239: What is the equation in standard form of a parabola whose vertex is (3,-1) and whose directrix is x=-2 ?
1.(y+1)^2=20(x-3)
2.(x+3)^2=20(y+1)
3.(x-3)^2=20(y+1)
4.(y-1)^2=20(x+3)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630)   (Show Source):
Answer by greenestamps(13215)  (Show Source):
You can put this solution on YOUR website!
The directrix is a vertical line, and it is to the left of the vertex, so the parabola opens to the right. That means the y variable is squared and the x variable is not. Since the question as you show it is multiple choice, that eliminates answer choices 2 and 3.
Note that NONE of the answer choices are in standard form. Standard form for a parabola opening right or left would be  . The answer choices are all in VERTEX form.
For a parabola that opens right or left, the vertex form of the equation contains (y-k)^2 and (x-h), where (h,k) is the vertex. Since the vertex is given to be (3,-1), the equation must contain "(y+1)^2" and "(x-3)". Again since the problem is multiple choice, there is only one answer choice which could possibly be the right equation -- answer choice 1.
To see that answer choice 1 is in fact the right equation, you need to look at the vertex form more closely. For a parabola opening to the right, the vertex form of the equation is
In this form, the vertex is (h,k), and p is the distance from the vertex to the directrix and from the vertex to the focus.
Answer choice 1 in vertex form is
So 4p=20, which means p is 5. And the directrix x=-2 is indeed 5 units to the left of the vertex; so answer choice 1 is the correct equation for the parabola.
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