completing the square to find centre and radius of the circle

[C17H13ClN4]

complete the square to find the centre and radius of this circle

x^2-5x+y^2+7x-9=0

 

[Deleted member 4993]

complete the square to find the centre and radius of this circle

x^2-5x+y^2+7x-9=0

I would start with the equation of a circle centered at (x₁, y₁) and centered at 'r'. The equation would be:

(x - x₁)² + (y - y₁)² = r²

Then I will "break-up" the given equation:

x^2-5x+y^2+7x-9=0

[x^2 - 2*(5/2)*x + (5/2)²] + [y^2 + 2*(7/2)*y + (7/2)²] - (5/2)² - (7/2)² - 9=0 .............[edited]

Continue....

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[Harry_the_cat]

Should it be 7y instead of 7x?

 

[HallsofIvy]

complete the square to find the centre and radius of this circle

x^2-5x+y^2+7x-9=0

Do you know what "complete the square" means?

How do you "complete the square" in x^2- 5x?

I suspect that the "7x" should be "7y".
How do you "complete the square" in y^2+ 7y?

(If it really is "7x" then someone is being really sneaky and it would be better
written as x^2+ 2x+ y^2- 9. That is actually easier!
It would be x^2+ 2x+ y^2= 9 so, adding 1 o both sides,
x^2+ 2x+ 1+ y^2= 10
(x+ 1)^2+ y^2= (x-(-1))^2+ (y- 0)^2= 10.
That is a circle with center at (-1, 0) and radius \(\displaystyle \sqrt{10}\).)

 

[Deleted member 4993]

Should it be 7y instead of 7x?

Please don't tell Jomo. Good catch.......fixed it ......