Question

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

Answer 1

please help

Answer 2

sec just making sure my numbers work

Answer 3

thank you ive narrowed it down to either a or c but i dont know what to do for there

Answer 4

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

Answer 5

(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

Answer 6

none of your options fit ...

Answer 7

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

Answer 8

I got that problem too.

Answer 9

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

Answer 10

its y value is the average of the focus y and the directrix

(5-11)/2 = -3

Answer 11

y = a(x+7)^2 - 3

Answer 12

a = 1/32

Answer 13

yep

Answer 14

can you screen shot it?

Answer 15

ya that's why I didn't reply faster... I was wondering if my math was bad or something haha

Answer 16

some people tend to post the answers for one with the question of another

Answer 17

oh my i am so sorry i realized the problem

Answer 18

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

Answer 19

never be afraid of your own errors ... they might prove to be correct int he end :)

Answer 20

Using either of the 2 methods posted above with the new data should give you the answer :)

Answer 21

thank yall sorry

Answer 22

Np.

Answer 23

good luck :)

Answer 24

so its a

Answer 25

thank you all so much that was very helpful