Answer:
[tex]x^2+y^2+1.54\cdot{x}-11.08\cdot{y}+13.86=0[/tex]
Step-by-step explanation:
We can use the general formula method:
[tex]x^2+y^2+2\cdot(g)\cdot{x}+2\cdot(f)\cdot{y}+c=0[/tex]
We substitute point 1 (6,3) into the equation:
[tex]6^2+3^2+12\cdot(g)+6\cdot(f)+c=0[/tex]
[tex]12\cdot(g)+6\cdot(f)+c=-45[/tex]
We substitute point 2 into the equation
[tex](-4)^2+(-3)^2-8\cdot(g)-6\cdot(f)+c=0[/tex]
[tex]-8\cdot(g)-6\cdot(f)+c=-25[/tex]
We know that he centre is (-g,-f) and we substitute it into equation y-2x-7=0
[tex]-f+2\cdot{g}-7=0[/tex]
We have 3 equations and we have 3 unknowns. We can eliminate c by subtracting the first two equations:
[tex]20\cdot(g)+12\cdot(f)=-20[/tex]
now we can solve in terms of f and g:
[tex]f=2\cdot{g}-7[/tex] into the above equation:
[tex]20\cdot(g)+24\cdot{g}-14=-20[/tex]
Solve for g:
[tex]g=0.77[/tex]
f is [tex]f=-5.45[/tex]
Therefore c is:
[tex]-8\cdot(0.77)-6\cdot(-5.45)+c=-25[/tex]
[tex]c=13.86[/tex]
The equation of the circle is:
[tex]x^2+y^2+1.54\cdot{x}-11.08\cdot{y}+13.86=0[/tex]
