Question

the equation of a circle is $x^2 + 4x + y^2 - 10y + 13 = 0$. what is the equation of the circle in standard form? $\circ (x + 4)^2 + (y - 25)^2 = 16$ $\circ (x + 4)^2 + (y - 25)^2 = 25$ $\circ (x + 2)^2 + (y - 5)^2 = 16$ $\circ (x + 2)^2 + (y - 5)^2 = 25$

Explanation:

Step1: Group x and y terms

$x^2 + 4x + y^2 - 10y = -13$

Step2: Complete square for x

$x^2 +4x +4 = (x+2)^2$, add 4 to both sides

Step3: Complete square for y

$y^2 -10y +25 = (y-5)^2$, add 25 to both sides

Step4: Combine constants

$-13 +4 +25 = 16$

Step5: Write standard form

$(x+2)^2 + (y-5)^2 = 16$

Answer:

C. $(x + 2)^2 + (y - 5)^2 = 16$