SOLUTION: what is the standard equation with a vertex of (2,3), and focus(2,5), with a directrix y=1

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Question 1184785: what is the standard equation with a vertex of (2,3), and focus(2,5), with a directrix y=1
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You could start with Distance Formula definition for parabola and work with the given directrix and focus, but there is also a shortcut formula for this.

%28x-2%29%5E2=8%28y-3%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Tutor @josgarithmetic has recently been giving a lot of responses that basically give the answer to a question without providing anything useful to the student who is trying to LEARN HOW to get the answer....

One version of the vertex form of a quadratic equation is

%28y-k%29=%281%2F%284p%29%29%28x-h%29%5E2

In that formula, (h,k) is the vertex and p is the directed distance (i.e., might be negative) from the vertex to the focus.

(Note in her response she uses the equivalent form

%28x-h%29%5E2=4p%28y-k%29

I have a personal preference for having the linear expression on the left side of the equals sign...)

In this problem we have the vertex (h,k)=(2,3), and p is the distance from (2,3) to (2,5), which is 2. That gives us the vertex form of the equation:

y-3=%281%2F8%29%28x-2%29%5E2

I leave it to you to convert that to standard form....