Question

Find the standard equation of the circle defined by the equation x^2 + y^2 +8x - 12y + 43 = 0. ANSWERS ATTACHED, due in 2 HOURS, will give Brainliest!

Answer 1

Answer:

Solution: Option C

Step-by-step explanation:

Our goal here is to factor the expression such that it is converted into the circle equation (x - a)² + (y - b)² = r² where r = radius centered at point (a,b).

$x^2\:+\:y^2\:+8x\:-\:12y\:+\:43\:=\:0$ (Factor the expression "x² + 8x")

$x^2+8x = x\left(x+8\right)$ (Factor the expression "y² - 12y")

$\:y^2-12y =y\left(y-12\right)$

That leaves us with the expression $\left(x-\left(-4\right)\right)^2+\left(y-6\right)^2=3^2$, or in other words $(x+4)^2 +(y-6)^2 = 9$. As you can see our solution is option c.