Question

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Answer 1

please explain too.

Answer 2

take any point on the parabola (x0,y0)
then the distance between this point and the focus is given by
sqrt[(x0 - 2)^2 + (y0 - 0)^2

and distance of the point from the directrix = 12

Answer 3

- sorry that distance from directrix is |y0 - 12|

Answer 4

so as the distance from the focus = distance from the directrix ( definition of a parabola) we have
sqrt[(x0 - 2)^2 + (y0 - 0)^2 = (0 -12)

simplify this to get the required equation

Answer 5

sorry - another typo its
sqrt[(x - 2)^2 + (y - 0)^2] = (y -12)

Answer 6

- I change x0 and y0 to x and y

Answer 7

squaring both sides
(x - 2)^2 + y^2 = (y - 12)^2
x^2 - 4x + 3 + y^2 = y^2 - 24y + 144

can you continue from here?

Answer 8

Could you go all the way please?

Answer 9

gave you best response

Answer 10

x^2 - 4x + 4 + y^2 = y^2 - 24y + 144
x^2 - 4x - 140 = -24y
y = (-1/24)x^2 + (1/6)x - 35/6 = 0

Answer 11

thanks.

Answer 12

I'm making a lot of typos today so I cant guarantee the answer but the method is right!

Answer 13

yeah its an answer could you help me with one more

Answer 14

no sorry gtg right now

Answer 15

I'm still not happy with that result

Answer 16

what result?

Answer 17

AH! the distance for directrix is |x - (-12)| = |x + 12|

so we have
(x - 2)^2 + y^2 = y^2 + 24x + 144
x^2 - 4x + 4 + y^2 = y^2 + 24y + 144
x^2 - 4x - 144 + 4 = 24x

y = (1/24)x^2 - (1/6)x - 144/24 = 0
y = (1/24)x^2 - (1/6)x - 35/6 = 0

is the correct answer

Answer 18

http://openstudy.com/study#/updates/55b3b8b7e4b071e6530e1ca4 \

Answer 19

the only problem with that is its not one of the options but I'm sure its correct

Answer 20

I'll check with wolfram alpha

Answer 21

lol wolfram

Answer 22

http://www.wolframalpha.com/input/?i=equation+of+a+parabola+with+focus+%282%2C0%29+and+directrix+y+%3D+-12

there you go
its correct

Answer 23

okay

Answer 24

come over here http://openstudy.com/study#/updates/55b3b8b7e4b071e6530e1ca4

Answer 25

so there must be a typo in one of the choices
looks like its C - which has 2 plus instead 2 negatives