Respuesta :
Answer:
Circle (ii) shifted 5 units left and 6 units up to get the circle (iii).
The radius of the circle is 2 units.
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
where, (h,k) is center and r is radius of the circle.
Consider the given equations of the circle are
[tex]x+y=4[/tex] ...(ii)
[tex](x+5)^2+(x-6)^2=4[/tex] ...(iii)
From (i) and (ii), we get
[tex]h=0,k=0,r^2=4\Rightarrow r=2[/tex]
So, the center of circle (ii) is (0,0) and radius is 2.
From (i) and (iii), we get
[tex]h=-5,k=6,r^2=4\Rightarrow r=2[/tex]
So, the center of circle (iii) is (-5,6) and radius is 2.
Therefore, the circle (ii) shifted 5 units left and 6 units up to get the circle (iii). The radius of the circle is 2 units.
