To find the equation of the circle with center (0, −1) that contains the point (−8, 10), we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Since the center of the circle is given as (0, −1), we have:
(x - 0)^2 + (y + 1)^2 = r^2
We still need to find the radius, r. We know that the circle passes through the point (−8, 10), so we can substitute these values for x and y and solve for r:
(-8 - 0)^2 + (10 + 1)^2 = r^2
64 + 121 = r^2
r^2 = 185
So the equation of the circle is:
x^2 + (y + 1)^2 = 185
Alternatively, we can expand the equation to get it in standard form:
x^2 + y^2 + 2y + 1 = 185
x^2 + y^2 + 2y - 184 = 0
So another form of the equation is:
x^2 + (y + 1)^2 = 185