Question

Choose ,begin emphasis,all,end emphasis, of the points where the graphs of the line y equals x minus 3 and the circle left-parenthesis x minus 1 right-parenthesis squared plus y squared equals 4 intersect.

Answer 1

The Solution:

Given:

$\begin{gathered} \left(x-1\right)^{2}+y^{2}=4 \\ y=x-3 \end{gathered}$

Required:

To determine all the points where the graphs of the two equations intersect.

Below is the graph of the two equations:

Clearly, we can see from the graph that the points the two equations intersect are:

$(3,0)\text{ and }(1,-2)$

Therefore, the correct answers are [options C and E]