Question

What are the coordinates of the focus of the conic section shown below? Y^2+16y+4x+4=0

Answer 1

please help i have to know how to do this by monday

Answer 2

Do you know how to complete the square?

Answer 3

isnt that when it factors perfectly?

Answer 4

yes, that's the idea.

first you need to move the 4x + 4 to the right of the equation
y^2 + 16y = -4x -4

Answer 5

then complete the square
y^2 +16y + 64 = -4x -4 + 64
(y+8)^2 = -4x +60
(y+8)^2 = 4 (-1) (x-15)
Does this look familiar now?

Answer 6

yes it sort of looks familiar

Answer 7

Standard form is (y-k)^2 = 4p (x-h)
Do you know which conics this is?

Answer 8

Parabola opens sideways

Answer 9

its in parabola form isn't it?

Answer 10

Correct !

Answer 11

ok so what is next?

Answer 12

Use the textbook formula to find focus?

Answer 13

which is( h+p, k)

Answer 14

(-15+?,8),

Answer 15

remember it's x- h and y - k
in this case h is postivie and y is negative because the original equation is (x+8)^2 = (4) (-1) (x-15)
)
so (15 + ?, -8)
p is -1

(15-1,- 8)

Answer 16

(14,-8) is the correct answer :o

Answer 17

That's what I got too :D

Answer 18

thank you for being awesome do you think you could help me with a few tomorrow?

Answer 19

Sure, what time though?
I have to go to church around 10 am to 4 pm tomorrow :P

Answer 20

I live in california so pacific time

Answer 21

ima try to wake up around 7 am pacific time

Answer 22

That's fine! I usually wake up around 6 am so I'll be there :D

Answer 23

ok ill fan you and thank you so much:D

Answer 24

welcome! It's 11:42 pm here so good night, and see you tomorrow.

Answer 25

alright you too