Question

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Answer 1

)find center and radius of -x^2+y^2+4y-16=0

Answer 2

You can start by grouping the y's together and then I believe that you have to complete the square for that one

Answer 3

I know its a hyperbola if that makes a difference

Answer 4

Well it's good that you know what the graph looks like

Answer 5

-x^2+4y^3-16=0 ??

Answer 6

looks like this
https://www.wolframalpha.com/input/?i=hyperbola+-x^2%2By^2%2B4y-16%3D0+

Answer 7

-x^2+y^2+4y-16=0

you should "complete the square" on this part: y^2 +4y
can you do that ?

Answer 8

\[y^2+4y-x^2=16\]
\[(y+2)^2-x^2=16+4=20\]
\[\frac{(y+2)^2}{20}-\frac{x^2}{20}=1\] i think

Answer 9

the distance from the center to the focus for either an ellipse or a hyperbola.

Answer 10

it wants to know the foci

Answer 11

First, what is the center ?

Answer 12

(0,-2)

Answer 13

next, what are a^2 and b^2

Answer 14

pattern match with the equation sat figured out for you.

Answer 15

compare to the standard equation for a hyperbola

Answer 16

a=2^2 ?

Answer 17

a^2=2^2

Answer 18

this it??

Answer 19

first, do you see sat's equation?
2nd, do you know the standard equation of a hyperbola ?
in this case
y^2/a^2 - x^2/b^2 = 1 (I left out the h,k stuff)

Answer 20

im confused?

Answer 21

i dont know the equation

Answer 22

for standard form

Answer 23

by standard form, I mean the version with a and b in it instead of numbers.

Answer 24

a^2+b^2=c

Answer 25

because you want to match it with your equation
\[ \frac{(y+2)^2}{20}-\frac{x^2}{20}=1 \]
to figure out what a^2 and b^2 are

Answer 26

does this remind you ?
http://www.mathwarehouse.com/hyperbola/graph-equation-of-a-hyperbola.php

Answer 27

a^2= 20 b^2=20 right ??

Answer 28

yes. next we use
a^2 + b^2 = c^2 **** notice it is c^2 not just c)

c is sometimes called the radius
can you find c ?

Answer 29

20+20=c^2

Answer 30

40=c^2

Answer 31

so far so good

Answer 32

now what?

Answer 33

take the square root of both sides
sqrt(c^2) is c (which is why we do this)
sqrt(40)= sqrt(2*2*10)= 2 sqrt(10) (this is the exact answer, but not convenient)
or about 6.32 using a calculator

Answer 34

c= 6.32

Answer 35

oh ok

Answer 36

c is the distance from the center to the focus

the center is (0,-2). we go up 6.32 to get to the focus (or down to get to the other one)
one focus is at (0,4.32)

(to do this, we need to know what this looks like, which is always a mystery to me until I plot it) but sat gave a link to a plot of it.

Answer 37

ok..

Answer 38

the question says
find center and radius

so are you done ?

Answer 39

no it wants the foci

Answer 40

can you work out the other one ?

Answer 41

what do u mean? i dont know how to find the foci

Answer 42

we have a "smiley/ frown" version
I gave you the focus for the smiley part.

look at this
https://www.wolframalpha.com/input/?i=hyperbola+-x^2%2By^2%2B4y-16%3D0+
and look at this
http://www.mathwarehouse.com/hyperbola/graph-equation-of-a-hyperbola.php
this one shows you where the foci are.

next remember that the focus is 6.32 away from the center.