Question

The equation of a circle in general form is x² + y² - 20x26y +244 = 0 What is the equation of the circle in standard form? O (x-10)² + (y – 13)² = 144 ○ (x-10)² + (y - 13)² = 25 (x-20)² + (y - 26)² = 25 (x - 20)² + (y-26)² = 144​

Answer 1

The equation of the circle in standard form is (x - 10)^2 + (y - 13)^2 = 25, obtained by completing the square for the x and y terms in the given general equation.

Step-by-step explanation:

The equation of the circle provided is x² + y² - 20x + 26y + 244 = 0. To convert this to standard form, we need to complete the square for both x and y.

First, group the x terms and the y terms: (x² - 20x) + (y² + 26y) = -244.

For the x terms, the coefficient to complete the square is (20/2)² = 10² = 100.

For the y terms, the coefficient to complete the square is (26/2)² = 13² = 169.

Add 100 and 169 to both sides of the equation and rewrite:

(x² - 20x + 100) + (y² + 26y + 169) = -244 + 100 + 169

this simplifies to:

(x - 10)² + (y - 13)² = 25

So, the equation in standard form is (x - 10)² + (y - 13)² = 25.