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)
Accepted Solution
A:
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