Question

What is the equation of a parabola with a focus of (8, –4) and a directrix of y = 2?

Answer 1

go to mathway it mat help you

Answer 2

@akshay1234 I already have reviewed all that information . I don't understand it .

Answer 3

@ganeshie8

Answer 4

i am unable to do

Answer 5

@annas

Answer 6

@a1234 @geekfromthefutur @hidy @lululife @minnie♥mouse @mathstudent55 @Mel98 @Zinda

Answer 7

Input points (8,-4) and (x, 2) into this formula:


\[\sqrt{(x - x_1)^2 + (y - y_1)^2} = \sqrt{(x - x_2)^2 + (y - y_2)^2}\]

Answer 8

\[\sqrt{(x - 8)^2 + (y - (-4))^2} = \sqrt{(x - x)^2 + (y - 2)^2}\]

Afterwards, square both sides:
\((x - 8)^2 + (y + 4)^2 = (x - x)^2 + (y - 2)^2\)

Answer 9

now Do I divide by the GCF ?

Answer 10

\(x^2 - 16x + 64 + y^2 + 8y + 16 = y^2 - 4y + 4\)

Answer 11

Then keep simplifying:

\(x^2 - 16x + 64 + 8y + 16 = -4y + 4\)

\((x - 8)^2 + 12 = -12y\)

\(-\dfrac{(x - 8)^2}{12} + 1 = y\)

Something like that

Answer 12

thats not a answer choice .

Answer 13

What are the answer choices?

Answer 14

y = -1/3(x-8)^2 -1
y = -1/3 (x+8)^2 -1
y = -1/12 (x-8)^2 - 1
y = -1/12 (x+8)^2 -1

Answer 15

That's the same thing except I made one tiny mistake

Answer 16

\(-\dfrac{(x - 8)^2}{12} - 1 = y\)

Answer 17

That's the same as

\(-\dfrac{1}{12}(x - 8)^2 - 1 = y\)

Answer 18

would it be the same answer if y was on the other side of the equation ?

Answer 19

Yes. In general If both sides are equal you can swap the information on both sides without changing the fact that they are equal:

\(x = a\) is the same as \(a = x\)

Answer 20

Find the equation of the parabola with a focus (2, 3) and directrix of y = 2.

Answer 21

@Hero

Answer 22

Follow the same method I demonstrated above.

Answer 23

Plug the points into the formula, then simplify until you have isolated y.

Answer 24

(x-2) ^2 + (y-3)^2 = (x-x)^2 + (y-2)^2
then you get ..
x^2 - 4x + 4 + 2y + 4 = 3y+3
iS THAT RIGHT SO FAR ?

Answer 25

You inserted the points correctly, but you made mistakes with the simplification.

Answer 26

can you help me ?

Answer 27

@Hero

Answer 28

Try to figure out what mistakes you made. If necessary start over from the beginning.

Answer 29

was all the simplifying wrong ? it all looks correct to me .

Answer 30

that doesn't seem right the choices are :
y = x^2/2 + 2x - 9/2
y = x^2/2 + 2x + 9/2
y = x^2/2 - 2x - 9/2
y = x^2/2 - 2x + 9/2

Answer 31

Hang on

Answer 32

Ok.

Answer 33

Double check to make sure you posted the correct information to begin with. Post it again just to be sure.

Answer 34

Actually, I thought about it. What I put was correct, just not in the form your problem wants.

Answer 35

can you help me put it in that form ?

Answer 36

\((x-2) ^2 + (y-3)^2 = (x-x)^2 + (y-2)^2\)

\(x^2 - 4x + 4 + y^2 - 6y + 9 = y^2 - 4x + 4\)

\(x^2 - 4x - 2y + 9 = 0\)

\(x^2 - 4x + 9 = 2y\)

\(\dfrac{x^2 - 4x + 9}{2} = y\)

\(\dfrac{x^2}{2} - 2x + \dfrac{9}{2} = y\)

Answer 37

@Hero can you help me with one more ? I can do it myself I just need you to check my work.
I can't afford to miss any problems.

Answer 38

Okay

Answer 39

Find the equation of the parabola with focus (5, 1) and directrix y = -1.

Answer 40

so far I got (x-5)^ + (y-1)^2 = (x-x)^2 + (y-2)^2
x^2 - 10x + 25 + y^2 -1y + 1 = y^2 - 10x + 25

Answer 41

The only part that is correct so far is x^2 - 10x + 25

Answer 42

I'm just copying how we did the last two problems . How am I still getting these wrong ?!

Answer 43

@Hero

Answer 44

@Hero This is timed .. please help me .. :(

Answer 45

@akshay1234 help please ?

Answer 46

what are you trying to find?

Answer 47

is this the problem
What is the equation of a parabola with a focus of (8, –4) and a directrix of y = 2?

Answer 48

Find the equation of the parabola with focus (5, 1) and directrix y = -1.

Answer 49

@satellite73

Answer 50

ok do me a favour and repost this question so i don't have to keep scrolling down
it is not very hard, we can do it in two or three steps