Write the standard equation for the circle center left parenthesis negative 6 comma negative 8 right parenthesis, that passes through left parenthesis 0 comma 0 right parenthesis.

Answer 1

The standard equation for a circle with center (-6, -8) passing through (0, 0) is:

(x + 6)^2 + (y + 8)^2 = r^2

where r is the radius of the circle. Since the circle passes through (0, 0), we can substitute these coordinates into the equation:

(0 + 6)^2 + (0 + 8)^2 = r^2
6^2 + 8^2 = r^2
36 + 64 = r^2
100 = r^2
r = 10

Therefore, the equation for the circle is:

(x + 6)^2 + (y + 8)^2 = 100