Nathan drew a circle on a grid with a radius of 4 units and the point (2, -1) as its center. Which of the following pairs of coordinates represent points on the circle?
(4, 0) and (0, 4)
(8, -4) and (6, -3)
(2, 3) and (-1, -1)
(2, -5) and (6, -1)

(2, -5) and (6, -1)

Step-by-step explanation:

The equation that represent the coordinate of a circle is  

(x-a)^2 + (y-b)^2 = r^2

Where

(a, b) is the coordinate of the center of the circle

r is the radius of the circle

The equation for the circle in this question will be:

(x-2)^2 + (y--1)^2 = 4^2

(x-2)^2 + (y+1)^2 =16

You can put each option into the equation and find it it's true. The points that will fulfill the condition is (2, -5) and (6, -1).  The calculation for each point will be:

(x-2)^2 + (y+1)^2 =16

(2-2)^2 + (-5+1)^2 =16

(0)^2 + (-4)^2 =16

16=16

true

(x-2)^2 + (y+1)^2 =16

(6-2)^2 + (-1+1)^2 =16

(4)^2 + (0)^2 =16

16=16

true

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )