Explain why the point A(7;2) does not lie on the circle x^2+y^2-16=0 .

To verify if a point is located on a circle, it's
coordinates must cancel the equation of the circle.

We'll
replace x and y with the values of coordinates of the point
A.

7^2 + 2^2 - 16 = 0

49 + 4 -
16 = 0

37 = 0 not true!

It is
obvious that the point is not located on the circle.

To
determine where exactly the point is found, we'll determine the power of the
point.

The power of A with respect to circle C
is:

p(A) = d^2 - r^2

d - is
the distance from A to the center of the circle C.

We'll
calculate d^2 = 7^2 + 2^2

d^2 = 49 +
4

d^2 = 53

p(A) = 53 -
16

p(A) = 37 >
0

Since the result of the power of the point
A, with respect to the circle C, is positive, the point is found outside the circle
C.