Question

HELP PLEASE!!
What is the focus of the parabola given by −1/4(y+2)^2=(x−1)?

Answer 1

a)(-1, 2)



b)(1, -2)



c)(0, -2)



d)(0, 2)

Answer 2

@Michele_Laino can you help please?

Answer 3

sorry is your parabola this?
\[-\frac{ 1 }{ 4(y+2)^{2} }=x-1\]

Answer 4

no, its the way i put it, in the question

Answer 5

@adamanderson

Answer 6

is this?
\[-\frac{ 1 }{ 4 }(y+2)^{2}=x-1\]

Answer 7

yes

Answer 8

ok! Now you have to change your coordinate system, namely you have to perform a traslation, whose equation are:
\[X=x-1,Y=y+2\]
where X and Y are the new coordinates.
In this new coordinate system, your parabola can be rewritten as below:
\[X=-\frac{ 1 }{ 4 }Y ^{2}\]

Answer 9

coordinates of focus of this parabola are simply to find, and are:
X=0, Y=0

Answer 10

but, please be careful, because we know X, and Y, and we have to know x and y instead.
In order to find x, and y, we have to substitute X=0 Y=0, in the above transformation equations, namely:
X=x-1, Y=y+2, so we have:
\[0=x-1,0=y+2\]
from which we can write:
x=1, and y=-2
so b).

Answer 11

took me awile but its (b

Answer 12

thanks so much!!!! couldnt have done without you!! @Michele_Laino

Answer 13

thanks!!!!!