Question

7. Which points are on the circle defined by the equation (x - 2)* + y = 9? Explain how you know.a.(-1,0)b. (5,0)(0, V5)d (3, 5)c.and beardils of the circle

Answer 1

The equation of the circle is defined by:

`(x-2)^2+y^2=9`

In order to determine the points that lie on the circle,

First, we need to substitute the value of x into the circle equation and solve for y. If the value of y obtained corresponds with the y-coordinate for that option, then we have our answers.

For [option a] with coordinates (-1, 0)

Put x = -1 into the circle equation

`\begin{gathered} (-1-2)^2+y^2=9 \\ (-3)^2+y^2=9 \\ 9+y^2=9 \\ y^2=9-9=0 \\ y=0 \end{gathered}`

For [option b] with coordinates (5, 0)

Put x = 5 into the circle equation

`\begin{gathered} (5-2)^2+y^2=9 \\ 3^2+y^2=9 \\ 9+y^2=9 \\ y^2=9-9=0 \\ y=0 \end{gathered}`

For [option c] with coordinates (0,√5)

Put x = 0 into the circle equation

`\begin{gathered} (0-2)^2+y^2=9 \\ (-2)^2+y^2=9 \\ 4+y^2=9 \\ y^2=9-4=5 \\ y=\sqrt[]{5} \end{gathered}`

For [option d] with coordinates (3, √5)

Put x = 3 into the circle equation

`\begin{gathered} (3-2)^2+y^2=9 \\ 1^2+y^2=9 \\ 1+y^2=9 \\ y^2=9-1 \\ y^2=8 \\ y=\sqrt[]{8} \end{gathered}`

Therefore, from our calculations, the options a, b, and c only are points on the circle because they satisfy the condition of the given equation of the circle.