Which of the following points is on the circle with the equation (x - 1)^2 + (y+2)^2 = 5.

Question

Which of the following points is on the circle with the equation (x - 1)^2 + (y+2)^2 = 5.

 

(1, -2)

 

(2, 2)

 

(3,-1)

 

(3, 4)

 

 

Answer 1

"Which of the following points     " might mean that there is more than one correct answer, so you must check all points:  for one correct answer, it might say, "which one of the following points ...:"

 

Let F = (x-1)^2+(y+2)^2

 

point       x     y     (x-1)    (y+2)    (x-1)^2    (y+2)^2      F        Is F=5?

-------   ----- -----  -----    -------  ----------    ---------     -----       ----------

(1, -2)     1    -2      0          0          0               0             0           No  

(2, 2)      2      2       1          4          1               16          17          No
(3,-1)      3     -1      2           1         4               1             5           Yes

(3, 4)      3      4       2          6         9               16           25          No   

Answer 2

(3,-1) ---> x=3 and y = -1

 

(3-1)^2 + (-1+2)^2 = 2^2 + 1^2 = 4+1 = 5

 

option C