Answer:
Point (20 , -3) lies on the circle ⇒ (A)
Explanation:
The point which lies on the circle must satisfy the equation of the circle
The equation of the circle is x² + (y - 12)² = 25²
Take the left hand side and substitute x and y by the coordinates of each point the answer must equal the right hand side
A. (20 , -3)
∵ x = 20
∵ y = -3
∴ (20)² + (-3 - 12)² = 400 + (-15)² = 400 + 225 = 625
∵ The right hand side is 25²
∵ 25² = 625
∴ The left hand side = The right hand side
∴ Point (20 , -3) satisfy the equation of the circle
∴ Point (20 , -3) lies on the circle
B. (-7 , 24)
∵ x = -7
∵ y = 24
∴ (-7)² + (24 - 12)² = 49 + (12)² = 49 + 144 = 193
∵ The right hand side is 25² = 625
∴ Point (-7 , 24) does not lie on the circle
C. (0 , 13)
∵ x = 0
∵ y = 13
∴ (0)² + (13 - 12)² = 0 + (1)² = 0 + 1 = 1
∵ The right hand side is 25² = 625
∴ Point (0 , 13) does not lie on the circle
D. (-25 , -13)
∵ x = -25
∵ y = -13
∴ (-25)² + (-13 - 12)² = 625 + (-25)² = 625 + 625 = 1250
∵ The right hand side is 25² = 625
∴ Point (-25 , -13) does not lie on the circle