Question

Circle O has a center at (1.-3) and a diameter of 8 units. Identify which point lies on Circle O. (15) (5,-3) (-6,5) (-2,-4)

Answer 1

The equation for a circle is given by:

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where:} \\ \text{center}=(h,k) \\ r=\text{radius}=(d)/(2) \end{gathered}`

so:

`\begin{gathered} d=8 \\ r=(8)/(2)=4 \\ C(h,k)=(1,-3) \\ (x-1)^2+(y+3)^2=16 \end{gathered}`

The point which lies on the circle will be the one which satisfies the equation, hence:

`\begin{gathered} (1,5) \\ (1-1)^2+(5+3)^2=16 \\ 64\\e16 \\ ------------------- \\ (5,-3) \\ (5-1)^2+(-3+3)^2=16 \\ 16=16 \end{gathered}`