Answer:
Radius , r = 5 units
Step-by-step explanation:
The standard form of a circle's equation:
[tex](x-a)^2 + (y -b)^2 = r^2 \ , \ where \ (a , b) \ is \ the \ centre\ and\ r \ is \ the \ radius.[/tex]
Given equation :
[tex]x^2 - 2x + y^ 2- 4y = 20\\\\[/tex]
Find radius .
Convert the given equation into standard form.
[tex](x - 1)^2 = x^ 2 - 2x + 1 \\\\(y - 2) ^2 = y^ 2 - 4y + 4\\\\[/tex]
Now add both equations :
[tex](x - 1)^2 + (y - 2)^2 = r^2[/tex]
[tex](x ^ 2 - 2x + 1) + (y^2 - 4y + 4 ) = r^2\\\\(x^2 -2x + y^2 - 4y ) + 1 + 4 = r^2\\\\20 + 1 + 4 = r^2[/tex] [tex][ \ given : \ x^2 - 2x + y^ 2 - 4y = 20 \ ][/tex]
[tex]25 = r^2 \\\\5 = r[/tex]
