Question

Which point does not lie on the circle centered at (3, 2) with radius 5? A) (0, 6) B) (3, -3) C) (-2, 2) D) (3, 0)

Answer 1

Answer:

D

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) = (3, 2) and r = 5, hence

(x - 3)² + (y - 2)² = 25 ← equation of circle

If an ordered pair lies on the circle then it satisfies the equation, if not then it does not lie on the circle.

Substitute the coordinates of the points into the left side of the equation of the circle and check validity.

A

(0 , 6) : (0 - 3)² + (6 - 2)² = 9 + 16 = 25 ← lies on circle

B

(3, - 3) : (3 - 3)² + (- 3 - 2)² = 0 + 25 = 25 ← lies on circle

C

(- 2, 2) : (- 2 - 3)² + (2 - 2)² = 25 + 0 = 25 ← lies on circle

D

(3, 0) : (3 - 3)² + (0 - 2)² = 0 + 4 = 4 ≠ 25 ← not on circle