tw101
  • tw101
Write the equation of the parabola with a focus (1,2) and directrix y = 1.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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tw101
  • tw101
Im not sure how to start.
tw101
  • tw101
1?
tw101
  • tw101
okay the formula you put up above?

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tw101
  • tw101
oh okay, onne second and then ill tell you what I got:)
jdoe0001
  • jdoe0001
one may note that 1,2 is the focus point, not the vertex point
tw101
  • tw101
oh wait what does that mean then?
jdoe0001
  • jdoe0001
well... she maybe crazy, but still beautiful, so tis ok =)
tw101
  • tw101
haha.
tw101
  • tw101
im seriously confused though...
jdoe0001
  • jdoe0001
|dw:1439942544203:dw|
tw101
  • tw101
Im not sure... Im sorry, this is new to me.
jdoe0001
  • jdoe0001
hmmm well.. have you covered parabolas yet?
tw101
  • tw101
Yes, briefly.
jdoe0001
  • jdoe0001
well.. it turns out that the focus point is "p" distance from the vertex and the directrix is "p" distance also from the vertex so.. the vertex is really half-way between both, since the focus and directrix are the same distance from the vertex keeping in mind that, the parabola opens up towards the focus point
tw101
  • tw101
Okay, well crazyandbeautiful helped me out and said that (1,3/2) was the vertex. haha.
jdoe0001
  • jdoe0001
hmmm how did she get 1, 3/2 though?
tw101
  • tw101
haha no you dont need to its okay! @Crazyandbeautiful
tw101
  • tw101
okay so its always halfway between the focus point and directrix?
jdoe0001
  • jdoe0001
yeap, they're always "p" distance from the vertex
tw101
  • tw101
Okay, i get that now:)
tw101
  • tw101
Where do I go from there?
jdoe0001
  • jdoe0001
so... get the vertex, get "p" and plug and chug \(\large{ \begin{array}{llll} (y-{\color{blue}{ k}})^2=4{\color{purple}{ p}}(x-{\color{brown}{ h}}) \\ (x-{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y-{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\\ {\color{purple}{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}}\)

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