Question

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)

Answer 1

B

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)

Answer 2

B.

R (2,4)

soln

center(h,k)=(6,1)

radius (r)=5units

so

eqn of circle is (x-6)^2+(y-1)^2=5^2

2 2

or, 25=x +y -12x-2y+36+1 now , only the given point (6,1)satisfies the eqn so this point lies on circle