Answer:
A) (20,-3)
Step-by-step explanation:
we know that
If a ordered pair lie on the circle, then the ordered pair must satisfy the equation of the circle
we have
![x^{2} +(y-12)^2=25^2](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%28y-12%29%5E2%3D25%5E2)
The center of the circle is the point (0,12) and the radius is r=25 units
<u><em>Verify </em></u>
A) (20,-3)
substitute the value of x and y in the equation and then analyze the result
![20^{2} +(-3-12)^2=25^2](https://tex.z-dn.net/?f=20%5E%7B2%7D%20%2B%28-3-12%29%5E2%3D25%5E2)
----> is true
therefore
The ordered pair lie on the circle
B) (-7,24)
substitute the value of x and y in the equation and then analyze the result
![-7^{2} +(24-12)^2=25^2](https://tex.z-dn.net/?f=-7%5E%7B2%7D%20%2B%2824-12%29%5E2%3D25%5E2)
----> is not true
therefore
The ordered pair not lie on the circle
C) (0,13)
substitute the value of x and y in the equation and then analyze the result
![0^{2} +(13-12)^2=25^2](https://tex.z-dn.net/?f=0%5E%7B2%7D%20%2B%2813-12%29%5E2%3D25%5E2)
----> is not true
therefore
The ordered pair not lie on the circle
D) (-25,-13)
substitute the value of x and y in the equation and then analyze the result
![-25^{2} +(-13-12)^2=25^2](https://tex.z-dn.net/?f=-25%5E%7B2%7D%20%2B%28-13-12%29%5E2%3D25%5E2)
----> is not true
therefore
The ordered pair not lie on the circle