In a circle, the point of symmetry is
the centerpoint; any straight line that passes through this point is a line of
symmetry. The standard form of equation of a circle is given as:
(x – h)^2 + (y – k )^2 = r^2
Where,
h = x coordinate of the center
k = y coordinate of the center
In the problem statement, we are given
that the equation of the circle is:
(x – 5)^2 + (y + 4)^2 = 25
So identifying the variables from the standard form of
equation of a circle:
h = 5
k = - 4
Therefore the point of symmetry is (5, -4).
