SOLUTION: The standard form equation of the parabola with vertex at (4, 1) and directrix x=2.

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Question 1170535: The standard form equation of the parabola with vertex at (4, 1) and directrix x=2.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
If distance from vertex to directrix is 2 units, then the focus is at (6,1).
Now you have the Directrix AND the Focus.

Use the Distance Formula definition for parabola and put the final equation into whichever form you need.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


With the vertex at (4,1) and the directrix the line x=2, the parabola opens to the right. The vertex form of the equation is then



where the vertex is (h,k) and p is the directed distance from the directrix to the vertex.

We are given (h,k) = (4,1); and p is the distance from the line x=2 to the point (4,1), which is 4-2=2. So p=2 and 4p=8. That gives us all the parts we need to write the equation:
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