The equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
The question seems incomplete and complete question given in the image !!!!
A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)
We know that the general equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where ( h, k ) is the center and r is the radius.
According to the question
The equation of circle given is [tex]x^2+y^2=1[/tex]
Center at origin
i.e
(h,k) = (0,0)
and radius = 1 unit
Now ,
By changing changing center (h,k) and radius of equation it will give following equations
h k r equation of circle
0 1 3 [tex](x-0)^2+(y-0)^2=3^2[/tex]
2 2 3 [tex](x-2)^2+(y-2)^2=3^2[/tex]
1 1 1 [tex](x-1)^2+(y-1)^2=1^2[/tex]
-2 -1 2 [tex](x+2)^2+(y+1)^2=2^2[/tex]
3 2 1 [tex](x-3)^2+(y-2)^2=1^2[/tex]
-5 1 3 [tex](x+5)^2+(y-1)^2=3^2[/tex]
Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
Learn more about general equation for a circle here
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