SOLUTION: Vertex (3,2) and Focus at (4,2)

Question 1203574: Vertex (3,2) and Focus at (4,2)
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Parabola? The symmetry axis is y=2, and is a horizontal line. Directrix is the line, x=2. Directrix can also be shown as a general "point" (2,y).

If you know the form of this equation then use that. If you are unsure but you know the Distance Formula definition of parabola, then,....

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Choosing the distance formula

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carry out the steps
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Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
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In his post, @josgarithmetic writes "Directrix is the horizontal line, x=2."

This wording is incorrect and can perplex/confuse you.

The correct wording, relevant to this problem, is "Directrix is a line, x=2."

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

Note it is poor practice to post relevant data without asking a question....

The focus is 1 unit to the right of the vertex, so the parabola opens to the right.

One form of the equation for that kind of parabola is

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

With the vertex at (3,2) and the focus 1 unit to the right, h=3, k=2, and p=1:

An alternative equivalent form is

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