Question

Select the correct answer.Which point lies on the circle represented by the equation x² + (y − 12)² = 25²?A. (20,-3)B. (-7,24)C. (0,13)D. (-25,-13)

Answer 1

We need to determine which of the given points lies on the circle with the equation:

`x^(2)+(y-12)^(2)=25^(2)`

In order to do so, we can replace x with the first coordinate of the point, and y with the second coordinate and see if the equation holds true.

A. For the point (20,-3), we have:

`\begin{gathered} 20^(2)+(-3-12)^(2)=25^(2) \\ \\ 400+15^(2)=625 \\ \\ 400+225=625 \\ \\ 625=625 \\ (TRUE) \end{gathered}`

Therefore, point (20,-3) lies on the circle.

For the other points, we have:

`\begin{gathered} (-7)^(2)+(24-12)^(2)=625 \\ \\ 49+144=625 \\ \\ 193=625 \\ (FALSE) \end{gathered}`
`\begin{gathered} 0^(2)+(13-12)^(2)=625 \\ \\ 1=625 \\ (FALSE) \end{gathered}`
`\begin{gathered} (-25)^(2)+(-13-12)^(2)=625 \\ \\ 625+625=625 \\ (FALSE) \end{gathered}`

Therefore, the only correct option is A: (20,-3).