Answer:
x=1
Step-by-step explanation:
2-3x=3x-4
6-3x=3x
6=6x
1=x
Answer:
The center of the circle is at;
![(1,-3)](https://tex.z-dn.net/?f=%281%2C-3%29)
The radius of the circle is;
![r=4](https://tex.z-dn.net/?f=r%3D4)
Explanation:
Given the equation of circle;
![x^2+y^2-2x+6y-6=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-2x%2B6y-6%3D0)
we want to re-write it in the form;
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
where;
![\begin{gathered} (h,k)\text{ is the center of the circle} \\ r\text{ is the radius} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28h%2Ck%29%5Ctext%7B%20is%20the%20center%20of%20the%20circle%7D%20%5C%5C%20r%5Ctext%7B%20is%20the%20radius%7D%20%5Cend%7Bgathered%7D)
Applying Completing the square method;
![\begin{gathered} x^2+y^2-2x+6y-6=0 \\ x^2-2x+1+y^2+6y+9=6+1+9 \\ (x-1)^2+(y+3)^2=16 \\ (x-1)^2+(y+3)^2=4^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%2By%5E2-2x%2B6y-6%3D0%20%5C%5C%20x%5E2-2x%2B1%2By%5E2%2B6y%2B9%3D6%2B1%2B9%20%5C%5C%20%28x-1%29%5E2%2B%28y%2B3%29%5E2%3D16%20%5C%5C%20%28x-1%29%5E2%2B%28y%2B3%29%5E2%3D4%5E2%20%5Cend%7Bgathered%7D)
comparing the derived equation to the general form we have;
![\begin{gathered} h=1 \\ k=-3 \\ r=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%3D1%20%5C%5C%20k%3D-3%20%5C%5C%20r%3D4%20%5Cend%7Bgathered%7D)
Therefore;
The center of the circle is at;
![(1,-3)](https://tex.z-dn.net/?f=%281%2C-3%29)
The radius of the circle is;
For your first question the answer is C(-2) and your next question the answer is A(-28)