Parabola with Focus (-5,0) & Vertex (-5,-4): Find Equation

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To find the equation of the parabola with a focus at (-5,0) and a vertex at (-5,-4), the correct form is derived from the standard equation for parabolas with vertical axes. The vertex form is y = a(x - h)² + k, where (h,k) is the vertex. The distance from the vertex to the focus determines the value of 'a', which is crucial for the equation. The initial equation proposed, x² + 10x + 16y + 89 = 0, is incorrect, and further steps are needed to derive the correct equation. A step-by-step approach is recommended to verify the calculations and ensure accuracy.
TonyC
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Fins an equation for the parabola with focus at (-5,0) and vertex at (-5,-4).

I have come up with:

x^2 + 10x + 16y + 89 = 0

How far off am I?
 
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TonyC said:
Fins an equation for the parabola with focus at (-5,0) and vertex at (-5,-4).

I have come up with:

x^2 + 10x + 16y + 89 = 0

How far off am I?

Can't you check for yourself?

Is it a parabola? (That's easy- there is an x2 term but no y2 term.)

What is the vertex? (Solve for y, then complete the square.)

What is the focus? (You will need to know the equation for the focus of a given parabola.)
 
That is what I am having trouble determining. Can you show me step by step how to check myself?
 
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