Question

find the equation of the circle with center $(-1, -1)$ and radius of 5.\
a $(x + 1)^2 + (y + 1)^2 = 25$\
b $(x + 1)^2 + (y - 1)^2 = 25$\
c $(x - 1)^2 - (y - 1)^2 = 5$\
d $(x - 1)^2 + (y - 1)^2 = 5$

Explanation:

Step1: Recall circle equation formula

The standard 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: Substitute center and radius

Given center \((-1, -1)\), so \(h = -1\), \(k = -1\), and radius \(r = 5\). Substitute into the formula: \((x - (-1))^2 + (y - (-1))^2 = 5^2\).
Simplify: \((x + 1)^2 + (y + 1)^2 = 25\).

Answer:

A. \((x + 1)^2 + (y + 1)^2 = 25\)