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anonymous
 one year ago
Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1
anonymous
 one year ago
Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0have you any method to use for this question...?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so what methods do you know.. 1. find the focal length and then find the vertex... 2. use the distance formula..

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0ok.... so start by plotting the given information dw:1437680444218:dw so this tells me the parabola is concave up... does that make sense...

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0ok... so the line of symmetry is x = 5 and the vertex is a units below the focus... where a = the focal length so dw:1437680607256:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the length between the focus and the directrix is 6

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0the distance between the focus and directrix is 2a the vertex is midway between the vertex and directrix on the line of symmetry

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0that's great so 2a = 6 therefore the focal length is a = 3 is that ok..?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437680777548:dw

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so where do you think the vertex is located..?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0woud it be at (5,2)

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0perfect.... now to get the correct equation I use a standard form \[(x  h)^2 = 4a(y  k)\] (h, k) is the vertex and a is the focal length so the equation is \[(x + 5)^2 = 4 \times 3 (y  2)\] so this can be simplified and rewritten in the form you need.

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0hope it all makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you, it really does help

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0if you need it rewritten I'd use \[y = \frac{1}{12}(x + 5)^2 + 2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's exactly what I thought it was. Thank you so much
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