Question

Find the centre and the radius of circle X^2 + Y^2 - 4X+6Y =3

Answer 1

Complete the square

Answer 2

\[x ^{2}+y ^{2}-4x+6y=3\]

Answer 3

Okay, so if you have \(y^2+6y\), then how do you complete the square?

Answer 4

\[
(y+c)^2 = y^2+2cy +c^2
\]

Answer 5

if \(2c=6\) then \(c = 3\) and \(c^2=9\)

Answer 6

This means that\[
(y+3)^2 = y^2+6y+9
\]

Answer 7

Or in other words: \[
y^2+6y = (y+3)^2-9
\]This is how you complete the square.

Answer 8

\[
x ^{2}+y ^{2}-4x+6y=3
\]Is the same as \[
x ^{2}-4x+(y+3)^2-9=3
\]

Answer 9

Now you need to complete the square for \(x^2-4x\).

Answer 10

ok let me see

Answer 11

i got it thank you very much, it's been a while since i touched any question with circles, needed to brush up.

Answer 12

r=4, C(2, -3)