Question

The general form of the equation of a circle is x2+y2+2x−6y+1=0. What are the coordinates of the center of the circle?

Answer 1

(-1,3)

Explanation:

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Answer 2

`x^(2) + y^2    + 2x  ⇒- 6y + 1 = 0`

≡
`x^(2) + y^(2) + 2fx + 2gy + c = 0`


`Centre = (-f, -g)`

From the equation given:

`2fx = 2x 2f = 2 f = 2/2 f = 1 -f = -1`

`2gy = -6y 2g = -6 g = -6 / 2 g = -3 -g = -(-3) -g = 3`

∴
`Centre = (-1, 3)`