Find an equation of the circle that has center (-2, 5) and passes through (-3, - 4).
The general equation of a circle is given by:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle and r is the radius.
Given that the center is (-2, 5), we can substitute these values into the equation:
(x + 2)^2 + (y - 5)^2 = r^2
Now, since the circle passes through (-3, -4), we can substitute these coordinates into the equation:
(-3 + 2)^2 + (-4 - 5)^2 = r^2
1^2 + (-9)^2 = r^2
1 + 81 = r^2
82 = r^2
Therefore, the equation of the circle is:
(x + 2)^2 + (y - 5)^2 = 82