toLet's begin by listing out the information given us:
[tex]\begin{gathered} origin=(4,3) \\ A\mleft(1,-1\mright),B\mleft(8,6\mright) \end{gathered}[/tex]
For a circle, we have the radius represented by r, the origin denoted by (h,k) with coordinates being (x, y)
To determine the equation of the line that goes through points A and B, we solve thus:
[tex]\begin{gathered} y=mx+b \\ m=\frac{\Delta y}{\Delta x}=\frac{6-(-1)}{8-1}=\frac{6+1}{7}=\frac{7}{7}=1 \\ We\text{ proceed to use the point-slope formula:} \\ y-y_1=m(x-x_1) \\ y-(-1)=(x-1)\Rightarrow y+1=x-1 \\ y=x-1-1\Rightarrow y=x-2 \\ y=x-2 \\ \\ \therefore The\text{ e}quation\text{ of the is given by, }y=x-2 \end{gathered}[/tex]
To determine if this line passes through the origin, we simply substitute the coordinate of the origin into the equation of the line:
[tex]\begin{gathered} y=x-2 \\ (x,y)=(4,3) \\ 3=4-2\Rightarrow3\ne2 \\ 3\ne2 \\ \therefore\text{This line does not pass through the center of the circle} \end{gathered}[/tex]
Therefore, this line does not pass through the center of the circle
