What is the equation of the circle with center (1, −1) that passes through the point (5, 7)?
A) (x + 1)2 + (y + 1)2 = 36
B) (x + 1)2 + (y − 1)2 = 52
C) (x − 1)2 + (y + 1)2 = 80
D) (x − 1)2 + (y − 1)2 = 100

Option C

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance from the center of the circle to any point on the circumference of the circle is equal to the radius of the circle

we have

(1,-1) and (5,7)

the formula to calculate the distance between two points is equal to

substitute the values

step 2

Find the equation of the circle in center radius form

where

(h,k) is the center

r is the radius

substitute

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.