Question

Which is an equation of a circle with center (-5, -7) that passes through the point (0, 0)?

a.) (x + 5)2 + (y + 7)2 = 74

b.) (x - 5)2 + (y - 7)2 = 74

c.) (x - 5)2 + (y - 7)2 = 37

d.) (x + 5)2 + (y + 7)2 = 37

Answer 1

First find the radius of the circle:

`r = \sqrt{(-5 - 0)^(2) + (-7 - 0)^(2) } \\ r = \sqrt{(-5)^(2) + (-7)^(2) } \\ r = √(25 + 49) \\ r √(74) \\ r^(2) = 74 \\ (x - (-5))^(2) + (y - (-7))^(2) = 74 \\ (x + 5)^(2) + (y + 7)^(2) = 74`