We are given an equation of a circle and a point. We are then asked to find if the point lies on the circle. The equation of the circle and the point is given below
[tex]\begin{gathered} \text{Equation of the circle} \\ (x+1)^2+(y-1)^2=16 \\ \text{Given point =(3,-1)} \end{gathered}[/tex]
To find if the point lies in the circle, we can use the simple method of substituting the coordinates into the equation of the circle.
This can be seen below:
[tex]\begin{gathered} (3+1)^2+(-1-1)^2=16 \\ 4^2+(-2)^2=16 \\ 16+4=16 \\ \therefore20\ne16 \end{gathered}[/tex]
Since 20 cannot be equal to 16, this implies that the point does not lie on the circle.
ANSWER: Option 3
