Question

@jim_thompson5910 how do i simplify this equation to find center and radius

x2 − 4x + y2 + 8y = −4

The center is located at (−2, −4), and the radius is 4.

The center is located at (2, −4), and the radius is 4.

The center is located at (−2, −4), and the radius is 16.

The center is located at (2, −4), and the radius is 16.

Answer 1

Do you know "Completion Of Square Method" ??

Answer 2

no

Answer 3

The equation of a circle on a coordinate plane is \[(x-h)^{2}+(y-k)^{2}=r ^{2}\]

Answer 4

h and k are the x and y coordinates of the center of the circle

Answer 5

@arilove1d she does not know completion of square method..

Answer 6

Do you want to learn the method @Gabylovesyou ??

Answer 7

\[x^2+y^2-4x+8y+4=0\]
compare with
\[x^2+y^2+2gx+2fy+c=0\]
center is (-g,-f) and radius is \[\sqrt{g^2+f^2-c}\]

Answer 8

@waterineyes sure

Answer 9

or you can use completing square method as suggested above.

Answer 10

@surjithayer great, I was earlier thinking the same when she said, she does not know the method.. :)

Answer 11

@Gabylovesyou can you use surjit's method? Can you apply?

Answer 12

im looking at it

Answer 13

Take your time. we are in no hurry.. :)

Answer 14

yea i have no idea.. i was trying to do my lessons example....
Step 1 [original equation]: x^2 - 4x + y^2 + 8y = -4
Step 2 [group like terms]: (x^2 - 4x) + (y^2 + 8y) = -4
Step 3 [complete the quadratics]:(x^2 - 4x + 4) + (y2 + 8y + 16) = -4 + (4 + 8)

Answer 15

idk if i did step 3 correctly...

Answer 16

What is this?

Answer 17

this is the way my lesson teaches it

Answer 18

Is this not Completion of square method?

Answer 19

i think it is

Answer 20

yes .. i just dont know how to do it lol

Answer 21

Step 3 [complete the quadratics]: You yourself typed it.. :P

Answer 22

complete the quadratics means the same as
complete the square

Answer 23

oh.. did i do it right ?

Answer 24

This is as simple as you log in to OS daily... :P

Answer 25

Okay, just one mistake.. You must add 16 on right hand side to balance your equation.. :)

Answer 26

didnt i do that ?

Answer 27

Step 3 [complete the quadratics]:(x^2 - 4x + 4) + (y2 + 8y + 16) = -4 + (4 + 8)

Not 8 in last but 16..

Step 3 [complete the quadratics]:(x^2 - 4x + 4) + (y2 + 8y + 16) = -4 + (4 + 16)

Answer 28

You did (4+8), you should do (4+16), getting?

Answer 29

ohh ok .. then it says this
Step 4 [simplify the equation]: (x2 − 4x+4) + (y2 + 8y+16) = 16
Step 5 [factor each quadratic]: (x - 2)^2 + (y + 4)^2 = 16^2
Step 6 [identify the center and radius]: (2,-4) radius 16 ?

Answer 30

so answer is D?

Answer 31

Do you still think radius is 16 ??

Answer 32

How you changed \(16\) to \(16^2\) there?

Answer 33

omg i ment 4^2 cx

Answer 34

That is right, don't do silly mistakes, go slow but correct.. :)

Answer 35

so answer is B....

Answer 36

So, \(B\) ??

Answer 37

yep.. :) Good.. :)

Answer 38

yes... lol thanks ! ;p