Question

I need explanation to the review, confused . Multi ~ answer

Answer 1

we know that

the center of the circle is (4,6) and the radius is 10 units

so

The equation of the circle is given by

`\begin{gathered} (x-4)^2+(y-6)^2=10^2 \\ (x-4)^2+(y-6)^2=100 \end{gathered}`

Remember that

If an ordered pair lie on the circle

then

the ordered pair must satisfy the equation of the circle

Verify each ordered pair

A ---> (-4,12)

For x=-4 and y=12

substitute in the equation of the circle

`\begin{gathered} (-4-4)^2+(12-6)^2=100 \\ (-8)^2+(6)^2=100 \\ 64+36=100 \\ 100=100\text{ ----> is true} \end{gathered}`

point A lies on the circle

B ----> (-6,6)

substitute in the equation

`\begin{gathered} (-6-4)^2+(6-6)^2=100 \\ -10^2+0=100 \\ 100=100 \end{gathered}`

Point B lies on the circle

C -----> (4,6)

Remember that (4,6) is the center

so

Point C does not lie on the circle

D ----> (13,10)

`\begin{gathered} (13-4)^2+(10-6)^2=100 \\ 9^2+4^2=100 \\ 81+16=100\text{ ----> is not true} \end{gathered}`

Point D does not lie on the circle

E -----> (4,16)

`\begin{gathered} (4-4)^2+(16-6)^2=100 \\ 0^2+10^2=100 \\ 100=100 \end{gathered}`

Point F lies on the circle

therefore

The answer are options

A, B, E