Question

the equation x^2+y^2-2x+6y+3=0 is equivalent to ?.... help please medal rewarded

Answer 1

you can write it down like this:
\[x^2-2x+1-1+y^2+6y+9-9+3=0\]
I added 1 and 9 and substracted 1and 9 so I didn't change the equation. Do you know what to do next?

Answer 2

how you can write x^2-2x+1 and y^2+6y+9 ?

Answer 3

wait what do you mean add and sub. 1 & 9?

Answer 4

i add and substract it because i want to use the square formula

Answer 5

\[x^2-2x+1=(x-1)^2\]

Answer 6

and \[y^2+6x+9=(y+3)^2\]

Answer 7

so our equation looks now like this:
\[(x-1)^2+(y+3)^2-1-9+3=0\]

Answer 8

so \[(x-1)^2+(y+3)^2=7\]

Answer 9

and this is equation of a circle

Answer 10

with center C=(1,-3) and radius sqrt7

Answer 11

i think i got it