Explanation:
the equation of a circle with (0, 0) as center is
x² + y² = r²
r being the radius.
therefore, the equation for our circle here is
x² + y² = 53.
now, we use the given point's coordinates for x and y in the equation :
(-3)² + (-7)² = 53
9 + 49 = 53
58 = 53
this is wrong, so the point does not lie on the circle.
the squares of the coordinates give a value (58) that is larger than the square of the radius (53), so the point is outside of the circle.
if smaller than the square of the radius, it would have been inside the circle.