Which point lies on a circle with a radius of 5 units and center at p(6, 1)?
a.
q(1, 11)
b.
r(2, 4)
c.
s(4, -4)
d.
t(9, -2)

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)

he has 140 chickens because he has 10 times more chickens than ducks and he has 14 ducks so 14*10=140