Question

write the standard form of the equation of the circle with the given center and radiu (-2,-4),3 o a (x - 4)^2 + (y - 2)^2 = 3 o b (x + 2)^2 + (y + 4)^2 = 9 o c (x - 2)^2 + (y - 4)^2 = 9 o d (x - 4)^2 + (y - 2)^2 = 3

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Identify the center coordinates

Given the center \((-2,-4)\), so \(h=-2\) and \(k = -4\).

Step3: Substitute into the standard form

Substituting \(h=-2\) and \(k=-4\) into \((x - h)^2+(y - k)^2=r^2\), we get \((x-(-2))^2+(y-(-4))^2=r^2\), which simplifies to \((x + 2)^2+(y + 4)^2=r^2\). Assuming \(r^2 = 9\) (since the problem might have a radius of 3, though radius is not clearly stated in the user - provided text but looking at the options, if we assume a radius of 3, the equation is \((x + 2)^2+(y + 4)^2=9\))

Answer:

B. \((x + 2)^2+(y + 4)^2=9\)