Answer:
the center of the circle, (h, k), is (3, -2),
and the radius is √18, or 3√2.
Step-by-step explanation:
This problem becomes much easier if you divide it through by 2:
x^2 - 6x +y^2 +4y = 5
Next, regroup this equation so that the x terms are together and the y terms are also together, separately:
x^2 - 6x + y^2 + 4y = 5
Next, complete the square of x^2 - 6x:
x^2 - 6x → x^2 - 6x + 9 - 9 → (x - 3)^2 - 9.
Then complete the square of y^2 + 4y:
y^2 + 4y + 4 - 4 → (y + 2)^2 - 4
Now rewrite x^2 - 6x + y^2 + 4y = 5 as
(x - 3)^2 - 9 + (y + 2)^2 - 4 = 5
Next, group the constants together on the right side:
(x - 3)^2 - 9 + (y + 2)^2 - 4 = 5 → (x - 3)^2 + (y + 2)^2 = 18
Comparing this result to the standard equation of a circle:
(x - h)^2 + (y - k)^2 = r^2,
we see that h = 3, y = -2 and r^2 = 18.
Thus, the center of the circle, (h, k), is (3, -2),
and the radius is √18, or 3√2.
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