Question

Please Answer ASAP ! Which point lies on the circle represented by the equation x2 + (y − 12)2 = 252?

Answer 1

Answer:

Point (20 , -3) lies on the circle ⇒ (A)

Step-by-step 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