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Step-by-step explanation:
The equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
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 - 1 )^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 .
To know more about general equation for a circle here:
https://brainly.com/question/10618691
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