Answer: The center of the circle is at the point (-21,-19), and its radius is [tex]\sqrt{849}[/tex] units.
The standard form of circle: [tex](x+21)^2+(y+19)^2=849[/tex]
Step-by-step explanation:
The given the equation of circle :-
[tex]x^2 + y^2 + 42x + 38y- 47 = 0[/tex]
The general equation of circle is given by :
[tex]x^2+y^2+2hx+2gy+a=0[/tex]
Here, the center of circle= (-h,-g)
and radius =[tex]\sqrt{h^2+g^2-a}[/tex]
Now, Comparing the given equation to the general equation, we get
[tex]2h=42\\\Rightarrow\ h=21\\\\2g=38\\\Rightarrow\ g=19[/tex]
Thus, the center of the given circle= (-21,-19)
Radius of given circle = [tex]\sqrt{21^2+19^2+47}=\sqrt{849}[/tex]
Now, the standard form of circle will be
[tex](x-(-21))^2+(y-(-19))^2=(\sqrt{849})^2\\\\\Rightarrow\ (x+21)^2+(y+19)^2=849[/tex]
