Question

Write x2 + y2 – 18x + 8y + 5 = 0 in standard form.

Group terms and move the constant to the other side of the equation.
x2 – 18x + y2 + 8y = –5
Determine the values that need to be added to both sides of the equation.
(–18 ÷ 2)2 = 81 and (8 ÷ 2)2 = 16
Add the values to both sides of the equation.
Write each trinomial as a binomial squared, and simplify the right side.
What is the standard form of the equation of a circle given by x2 + y2 – 18x + 8y + 5 = 0?

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Answer 1

Start with
x^2 + y^2 − 18x + 8y + 5 = 0
Group and move constant:
x^2 − 18x + y^2 + 8y = −5
Complete the square: add 81 and 16 to both sides (because (−18/2)^2 = 81, (8/2)^2 = 16):
(x^2 − 18x + 81) + (y^2 + 8y + 16) = −5 + 81 + 16
Write as squares and simplify:
(x − 9)^2 + (y + 4)^2 = 92

So the standard form is (x − 9)^2 + (y + 4)^2 = 92. The center is (9, −4) and the radius is sqrt(92) = 2√23.