Question

find the equation of the line that passes through the centers of the circles with equation x^2+y^2-6x+8y+13=0 and x^2+y^2-2y-3=0

Answer 1

Find the center of each circle by converting to standard form
\[x^2-6x+9+y^2+8y+16=-13+9+16\]\[(x-3)^2+(y+4)^2=12\]Center of first circle is (3,-4)
Find center of second circle
\[x^2+y^2-2y+1=3+1\]\[x^2+(y-1)^2=4\]Center of second circle is (0,1)

(Continued...)

Answer 2

Find the slope of the line\[m=\frac{-4-1}{3-0}=\frac{-5}{3}\]Use point slope and the second center since it contains a 0 coordinate
\[y-1=-\frac{5}{3}(x-0)\]solve for y\[y=-\frac{5}{3}x+1\]

Answer 3

how did u get the 16 and 9

Answer 4

?

Answer 5

do you know how to complete the square?

Answer 6

oh! is that what u did there?

Answer 7

I completed the square on the x-variables (the 9) and the y variables (the 16) separately

Half of 6 squared is 9
x^2-6x+9
Now it is a perfect square trinomial

Answer 8

thanks dear,which country u from?

Answer 9

Italia, living in US right now

Answer 10

school :})

Answer 11

ok,good knowing u.
am from nigeria,studying in canada

Answer 12

we are neighbors!

Answer 13

hahaha yeah

Answer 14

i don't know if u can be helping me out in my assignments,especially physics and math

Answer 15

Someone must be a Superman fan

Answer 16

physics :{(
math :})

Answer 17

lool ok only math,am good at physics as well

Answer 18

yo am going offline man catch u later
u can add me on facebook (krypton krish)