We have a circle represented by the equation:
[tex](x-4)^2+(y-2)^2=7^2=49[/tex]Any point that satisfy the equation of the circle lies in the circumference of the circle.
We can test each point by replacing the values of x and y in the equation by the coordinates of the point.
A) (-1,4)
[tex]\begin{gathered} (-1-4)^2+(4-2)^2=49 \\ (-5)^2+2^2=49 \\ 25+4=49 \\ 29\neq49 \end{gathered}[/tex]The point (-1,4) does not lie in the circle.
B) (8,3)
[tex]\begin{gathered} (8-4)^2+(3-2)^2=49 \\ 4^2+1^2=49 \\ 16+1=49 \\ 17\neq49 \end{gathered}[/tex]The point (8,3) does not lie in the circle.
C) (9,0)
[tex]\begin{gathered} (9-4)^2+(0-2)^2=49 \\ 5^2+(-2)^2=49 \\ 25+4=49 \\ 29\neq49 \end{gathered}[/tex]The point (9,0) does not lie in the circle.
D) (-2,2)
[tex]\begin{gathered} (-2-4)^2+(2-2)^2=49 \\ (-6)^2+0^2=49 \\ 36+0=49 \\ 36\neq49 \end{gathered}[/tex]The point (-2,2) does not lie in the circle.
