Answer:
The equation of the circle with centre (h,k) and radius (r) can be written as :-
[tex] \\ \qquad \sf \: {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ [/tex]
So, we are given with :-
Now, by putting their value we can write the equation as :-
[tex] \\ \qquad\sf \: {(x - 2)}^{2} - {(y - 6)}^{2} = {4}^{2} (16) \\ [/tex]
Expanding this, we get :-
[tex] \\ \sf {x}^{2} - 4x + 4 + { y}^{2} - 12y + 36 = 16 \\ [/tex]
Rearranging and by subtracting by 16 from both sides we got standard polynomial as -
[tex] \\ \sf \: {x}^{2} + {y}^{2} - 4x - 12y + 20 = 0 \\ [/tex]
