Question

The general form of a circle is given as x^2+y^2+4x - 12y + 4 = 0. A) What are the coordinates of the center of the circle? B) What is the length of the radius of the circle? ( Please Do Not Repost Someone Else's Answers On Brainly Or Any Other Websites Please If So You'll Be Reported). Will Mark Brainliest if answered correctly and please be honest . ​

Answer 1

Answer:

center = (-2, 6)

radius = 6

Step-by-step explanation:

Equation of a circle

$(x-a)^2+(y-b)^2=r^2$

(where (a, b) is the center and r is the radius)

Therefore, we need to rewrite the given equation into the standard form of an equation of a circle.

Given equation:

$x^2+y^2+4x-12y+4=0$

Collect like terms and subtract 4 from both sides:

$\implies x^2+4x+y^2-12y=-4$

Complete the square for both variables by adding the square of half of the coefficient of $x$ and $y$ to both sides:

$\implies x^2+4x+\left(\dfrac{4}{2}\right)^2+y^2-12y+\left(\dfrac{-12}{2}\right)^2=-4+\left(\dfrac{4}{2}\right)^2+\left(\dfrac{-12}{2}\right)^2$

$\implies x^2+4x+4+y^2-12y+36=-4+4+36$

Factor both variables:

$\implies (x+2)^2+(y-6)^2=36$

Therefore:

• center = (-2, 6)
• radius = √36 = 6