Question

A conic section has the equation x^2+ y^2+ 12x + 8y = 48. Determine the following: type of conic, domain and range, axes of symmetry, and center. Show your work.

Answer 1

@ganeshie8

Answer 2

it is circle .. circle has the form \[x ^{2}+y ^{2}+ax+by+c=0\]

Answer 3

center (-6,-4) and radius 2

Answer 4

how did you get 2 for the radius?

Answer 5

@crazysingh is correct! :D

Answer 6

if the circle equation is of the form \[x^{2} + y ^{2} + 2gx + 2fy + c = 0 \] then radius is equal to \[\sqrt{g ^{2}+f ^{2}-c}\]

Answer 7

radius should be 10 rihgt ?b

Answer 8

http://www.wolframalpha.com/input/?i=center+++x%5E2%2B+y%5E2%2B+12x+%2B+8y+%3D+48

Answer 9

domain is \[x \in (-8,-4)\]

Answer 10

just check the work again..

Answer 11

yes radius should be 10

Answer 12

clearly its a circle,

Answer 13

domain wud be \(center \pm radius\)

Answer 14

so domain = \(\large [ -16, 4]\)

Answer 15

@ganeshie8 : isnt \[domain = x coordinate of center \pm radius\]

Answer 16

good catch, yes :)

Answer 17

lets find range

Answer 18

\[range = y coordinate of center \pm radius\]

Answer 19

so the domain is not -16, 4?

Answer 20

domain is represented by \[{ x : -16 \le x \le4 }\]

Answer 21

ok..and how would we find the range?

Answer 22

range is represented by \[{y: -14 \le y \le 6 }\]

Answer 23

ok..what about the axis of symmetry?

Answer 24

there are infinite numbers of axis of symmetry which passes through center of this circle.. i.e. every line which passes through center of the circle represents axis of symmetry.

Answer 25

it will have the form : \[(y+6)=m(x+4)\]

Answer 26

wait..when you say the form, is that how i would put it down as my answer? or do i need to do something with it?

Answer 27

i guess there is no need to edit..

Answer 28

ok..thankyou:)

Answer 29

you should understand question rather than just copying

Answer 30

i do, and im not "just copying" i was looking at your steps and trying to learn how you did it....

Answer 31

ok sowiee..