Question

which of the following is the equation of a circle with center (0, -1) and radius 6?
a. $x^{2}+(y + 1)^{2}=36$
b. $x^{2}+y^{2}=12$
c. $x^{2}+y^{2}=36$
d. $x^{2}+(y + 1)^{2}=12$

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the values of \(h\), \(k\), and \(r\)

Given that the center is \((0,-1)\), so \(h = 0\), \(k=-1\), and the radius \(r = 6\).

Step3: Substitute the values into the formula

Substitute \(h = 0\), \(k=-1\), and \(r = 6\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 0)^2+(y-(-1))^2=6^2\), which simplifies to \(x^{2}+(y + 1)^{2}=36\).

Answer:

A. \(x^{2}+(y + 1)^{2}=36\)