SOLUTION: How do you write the equation of a parabola based on this information? Directrix=-3 ; Focus (3,5)

Question 456438: How do you write the equation of a parabola based on this information?
Directrix=-3 ; Focus (3,5)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How do you write the equation of a parabola based on this information?
Directrix=-3 ; Focus (3,5)
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Note: I believe you meant the directrix to be written as x=-3, not just 3. The directrix is a line so it is expressed as an equation.
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The axis of symmetry is always perpendicular to the directrix so the axis of symmetry is horizontal at y=5. Parabola opens rightwards. Standard form for this parabola:
(y+k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex, and p=distance between vertex and focus on the line of symmetry.
p=3
vertex(0,5)
Equation of given parabola:
(y-5)^2=12x
see graph below as a visual check on the answer.
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y=(12x)^.5+5

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