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

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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

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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please help
sec just making sure my numbers work
thank you ive narrowed it down to either a or c but i dont know what to do for there

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Other answers:

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
(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
none of your options fit ...
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
I got that problem too.
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
its y value is the average of the focus y and the directrix (5-11)/2 = -3
y = a(x+7)^2 - 3
a = 1/32
yep
can you screen shot it?
ya that's why I didn't reply faster... I was wondering if my math was bad or something haha
some people tend to post the answers for one with the question of another
oh my i am so sorry i realized the problem
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
never be afraid of your own errors ... they might prove to be correct int he end :)
Using either of the 2 methods posted above with the new data should give you the answer :)
thank yall sorry
Np.
good luck :)
so its a
thank you all so much that was very helpful

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