Question

Which of the following points lie on the circle whose equation is (x - 3)² + (y + 1)² = 20? Select all that apply.

Answer 1

Points that lie on the circle: (7, -3) and (-1, 1)

Answer 2

Substititute the points in the equation to check which point lie on the circle.

`\begin{gathered} (13-3)^2+(-1+1)^2=20 \\ (10)^2=20 \\ 100\\e20 \end{gathered}`

Point (7,-3),

`\begin{gathered} (7-3)^2+(-3+1)^2=20 \\ 16+4=20 \\ 20=20 \end{gathered}`

Point (7,-3) lies on the circle.

For point (5,-3),

`\begin{gathered} (5-3)^2+(-3+1)^2=20 \\ 4+4=20 \\ 8\\e20 \end{gathered}`

For point (-1,1),

`\begin{gathered} (-1-3)^2+(1+1)^2=20 \\ (-4)^2+(2)^2=20 \\ 16+4=20 \\ 20=20 \end{gathered}`

Point (-1,1) lie on the circle.

For point (1,-3),

`\begin{gathered} (1-3)^2+(-3+1)^2=20 \\ 4+4=20 \\ 8\\e20 \end{gathered}`

So points lie on the circle are (7,-3) and (-1,1).