Question

If the center of a circle is (1, 1), and it has a radius of 5, which is another point on the circle? A) (7, 1) B) (1, -5) C) (4, 5) Eliminate D) (-2, 6)

Answer 1

C

Explanation:

Answer 2

we know that

the equation of a circle is
(x-h)²+(y-k)²=r²
where
(h, k) ---------> is the center of a circle
r-----------> is the radius
so
(h, k)-------- (1, 1)
r=5
(x-1)²+(y-1)²=25

which is another point on the circle?
A) (7, 1)
(7-1)²+(1-1)²=25---------> (6)²+(0)²----> 36 is not 25
point A is not on the circle

B) (1, -5)
(1-1)²+(-5-1)²=25---------> (0)²+(-6)²----> 36 is not 25
point B is not on the circle

C) (4, 5)
(4-1)²+(5-1)²=25---------> (3)²+(4)²----> 9+16------> 25=25
point C is on the circle

D) (-2, 6)
(-2-1)²+(6-1)²=25---------> (-3)²+(5)²----> 9+25------> 34 is not 25
point D is not on the circle

the answer is
the point C) (4, 5) is on the circle