Question

Find the equation of the circle in standard form:

Answer 1

Explanation:

Standard form is

(x - h)^2 + (y - k)² = r²

(h, k) is the center

r is the radius

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x² + y² - 8x + 4y = -11

Regroup

(x² - 8x) + (y² + 4y) = -11

Complete the square for x

(x - 4)² + (y² + 4y) = -11 + (-4)²

Complete the square for y

(x - 4)² + (y + 2)² = -11 + (-4)² + 2²

Simplify

(x - 4)² + (y + 2)² = 9

Instandard form

(x - 4)² + (y + 2)² = 3²

Answer 2

In standard form, the answer is =

`(x - 4 {)}^(2) + (y + 2 {)}^(2) = 9`