SOLUTION: for a parabola given with the vertex (3,4) and focus (3,6) write an equation. how would I get started when solving this?

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Question 1081477: for a parabola given with the vertex (3,4) and focus (3,6) write an equation. how would I get started when solving this?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
The directrix is the line, y=2, which you might express as a general point (x, 2).



One of these methods will work for you:
derive equation of parabola given focus and directrix, vertex not at Origin

Vertex at the origin,
derive equation for parabola, given focus and directrix

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

for a parabola given with the vertex (3,4) and focus (3,6) write an equation. how would I get started when solving this?
1) The coordinates of the vertex, or (h, k) are: (3, 4) 

2) Use (h, k) and the focus: (h, p + k) to find p

3) Substitute values for h, k, and p into the CONIC FORM of a parabola with a vertical axis of symmetry, or %28x+-+h%29%5E2+=+4p%28y+-+k%29. 

   You should get the equation in CONIC form: highlight_green%28%28x+-+3%29%5E2+=+8%28y+-+4%29%29, or in VERTEX form: highlight_green%28matrix%281%2C3%2C+y%2C+%22=%22%2C+%281%2F8%29%28x+-+3%29%5E2+%2B+4%29%29