anonymous
  • anonymous
Derive the equation of the parabola with a focus at (−7, 5) and a directrix of y = −11. a) f(x) = −one eighth (x − 2)2 + 6 b)f(x) = one eighth (x − 2)2 + 6 c)f(x) = −one eighth (x + 2)2 + 8 d)f(x) = one eighth (x + 2)2 + 8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
please help
anonymous
  • anonymous
sec just making sure my numbers work
anonymous
  • anonymous
thank you ive narrowed it down to either a or c but i dont know what to do for there

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More answers

amistre64
  • amistre64
one method is to define all points (x,y) that are equidistance from a focus (a,b) and a directrix (in this case y=k) - which is just the point (x,k) (x-a)^2 + (y-b)^2 = (x-x)^2 + (y-k)^2
amistre64
  • amistre64
(x-a)^2 + y^2 -2by +b^2 = y^2 -2ky +k^2 (x-a)^2 -2by +b^2 = -2ky +k^2 (x-a)^2 +(b^2-k^2) = 2by -2ky (x-a)^2 +(b^2-k^2) = 2(b-k)y (x-a)^2/(2(b-k)) +(b^2-k^2)/(2(b-k)) = y (x-a)^2/(2(b-k)) +(b+k)/2 = y
amistre64
  • amistre64
none of your options fit ...
anonymous
  • anonymous
if you use the formula \[y=a(x-h)^2+k \] where P = -7 Q = 5 and R = -11 and where a = \[\frac{ 1 }{ 2Q-2R }\] H = P and \[K = \frac{ Q + R }{ 2 }\] you can just plug in the values and solve
anonymous
  • anonymous
I got that problem too.
amistre64
  • amistre64
we know the options are bad or something off, since the parabola opens up its vertex x is the same value as the focus x ... (x+7)^2 is the main part
amistre64
  • amistre64
its y value is the average of the focus y and the directrix (5-11)/2 = -3
amistre64
  • amistre64
y = a(x+7)^2 - 3
anonymous
  • anonymous
a = 1/32
amistre64
  • amistre64
yep
amistre64
  • amistre64
can you screen shot it?
anonymous
  • anonymous
ya that's why I didn't reply faster... I was wondering if my math was bad or something haha
amistre64
  • amistre64
some people tend to post the answers for one with the question of another
anonymous
  • anonymous
oh my i am so sorry i realized the problem
anonymous
  • anonymous
two of the questions were switched because those look like they would work for Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8
amistre64
  • amistre64
never be afraid of your own errors ... they might prove to be correct int he end :)
anonymous
  • anonymous
Using either of the 2 methods posted above with the new data should give you the answer :)
anonymous
  • anonymous
thank yall sorry
anonymous
  • anonymous
Np.
amistre64
  • amistre64
good luck :)
anonymous
  • anonymous
so its a
anonymous
  • anonymous
thank you all so much that was very helpful

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