Answer:
[tex](x - 2)^{2} + (y - 1)^{2} = 17[/tex]
Step-by-step explanation:
The current equation of the circle is:
⇒ [tex]x^{2} + y^{2} - 4x - 2y + 10 = 0[/tex]
In order to get it into the standard form;
⇒ [tex](x - a)^{2} + (y - b)^{2} = r^{2}[/tex]
We must complete the square;
⇒ [tex](x - 2)^{2} - 4 + (y - 1) - 1 + 10 = 0[/tex]
Now, collect like terms and rearrange;
⇒ [tex](x - 2)^{2} + (y - 1)^{2} = -5?[/tex]
We now know that the Centre is at the point (2, 1).
We can use the distance formula to find the radius;
⇒ [tex]d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]
⇒ [tex]d = \sqrt{(6 - 2)^{2} + (2 - 1)^{2}}[/tex]
⇒ [tex]\sqrt{17}[/tex]
Therefore the radius squared is 17.
Now substitute into our equation:
⇒ [tex](x - 2)^{2} + (y - 1)^{2} = 17[/tex]
