Question

Which point does not lie on the circle centered at (3, 2) with radius 5?

Answer 1

The complete question in the attached figure

we know that
the equation of a circle is

(x-h)²+(y-k)²=r²
where
(h,k) is the center
and
r is the radius
so
(x-h)²+(y-k)²=r²------> (x-3)²+(y-2)²=5²

case A) point (0,6)
for x=0  and y=6
(0-3)²+(6-2)²=5²------> 9+16=5²-----> 25=25
the point lie on the circle

case B) point (3,-3)
for x=3  and y=-3
(3-3)²+(-3-2)²=5²------> 0+25=5²-----> 25=25
the point lie on the circle

case C) point (-2,2)
for x=-2  and y=2
(-2-3)²+(2-2)²=5²------> 25+0=5²-----> 25=25
the point lie on the circle

case D) point (3,0)
for x=3  and y=0
(3-3)²+(0-2)²=5²------> 0+4=5²-----> 4 is not 25
the point not lie on the circle

the answer is
point (3,0)  not lie on the circle