Acircle with center c(4, -2) passes through the point a(1, 3). does the point b(8, -2) lie inside the circle?

Yes, point B will lie inside the circle.

Step-by-step explanation:          

Let the distance between point C and point A be the radius of our given circle.

We have been given that a circle with center C(4, -2) passes through the point A(1, 3).  

Since we know that a point will lie inside circle if the distance between the point and center of circle is less than radius of circle.

Let us find distance between points C and A using distance formula.

Radius of our circle is . Now let us find distance between center of our circle and point B.

We can see that distance of point B from center of our given circle is less than distance between point A and center of circle, therefore point B will lie inside the circle.

the correct answer is the second option