Question

How would I write an equation for a parabola with the focus being (0,-1/17). The vertex is set at the origin.

Answer 1

well.... if the vertex is at the origin

how far is the focus from the vertex?

Answer 2

a is usually the distance between the vertex to focus

Answer 3

in standard for it's usually +/-4a

Answer 4

well.... but in this case we have a focus point
and we have a vertex point too :)

so... I'd think we know the distance between both

Answer 5

mm...would you use the distance formula? Using the given points?

Answer 6

well.... you could do that... or you can just graph them and notice it

Answer 7

so... how far do you think the focus is from the vertex?

Answer 8

approximately (0,-.06)

Answer 9

well... yes to be exact 1/17 :)

so \(\bf (y-{\color{brown}{ k}})^2=4{\color{blue}{ p}}(x-{\color{brown}{ h}})\implies (y-{\color{brown}{ 0}})^2=4{\color{blue}{ \left(\frac{1}{17}\right)}}(x-{\color{brown}{ 0}})\)

notice the focus is "below" the vertex, so we know is a "vertical" parabola
and since the focus is below, then it has a negative "p" distance
p= distance of the focus to vertex
thus \(\bf (y-{\color{brown}{ 0}})^2=4{\color{blue}{ \left(-\frac{1}{17}\right)}}(x-{\color{brown}{ 0}})\)

Answer 10

Thank you, I was concerned about how I was going to Incorporated the vertex. I always have a difficult time incorporating the origin when it's at (0,0).

Answer 11

yw