Answer:
B
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (6, 1) and r = 5, thus
(x - 6)² + (y - 1)² = 25 ← equation of circle
To determine which point lies on the circle, substitute the coordinates into the left side and if equal to the right side then point is on the circle
A (1, 11)
(1 - 6)² + (11- 1)² = (- 5)² + 10² = 25 + 100 = 125 ≠ 25 ← not on circle
B (2, 4)
(2 - 6)² + (4 - 1)² = (- 4)² + 3² = 16 + 9 = 25 ← lies on circle
C (4, - 4)
(4 - 6)² + (- 4 - 1)² = (- 2)² + (- 5)² = 4 + 25 = 29 ≠ 25 ← not on circle
D (9, - 2)
(9 - 6)² + (- 2 - 1)² = (- 3)² + (- 3)² = 9 + 9 = 18 ≠ 25 ← not on circle
The only point that lies on the circle is R(2, 4)
