Answer:
[tex]x^{2} + y^{2} -10x -16y + 39[/tex]
Step-by-step explanation:-
The equation used to find the equation of circle is :-
[tex](x-a)^{2} + (y-b)^{2} = radius^{2}[/tex]
'a' means the x coordinate of the circle, 'b' means y coordinate of the circle.
In the question, it's given that the coordinates of the circle are (5, -8) and radius is 8cm.
So, 'a' will be 5 and 'b' will be -8
So,
[tex](x-5)^{2} + (y--8)^{2} = 8^{2}[/tex]
[tex](x-5)^{2} + (y+8)^{2} = 64[/tex]
[tex]x^{2} - 10x + 25 + y^{2} - 16y + 64[/tex]
[tex]x^{2} + y^{2} -10x -16y + 64 - 25[/tex]
= [tex]x^{2} + y^{2} -10x -16y + 39[/tex]
