Answer :
The locus of the centers of all circles of a given radius a, in the same plane, passing through a fixed point, is [tex](x-s)^{2}[/tex] + [tex](y-b)^{2}[/tex] = [tex]a^{2}[/tex]
Let the center of the circle (h,b)
and fixed point (s,t)
Distance between the center and fixed point = radius
[tex]\sqrt{(h-s)^{2} +(t-b)^{2} }[/tex] = a
[tex](h-s)^{2}[/tex] + [tex](t-b)^{2}[/tex] = [tex]a^{2}[/tex]
Here locus of the center is a circle having the center as a fixed point.
[tex](x-s)^{2}[/tex] + [tex](y-b)^{2}[/tex] = [tex]a^{2}[/tex]
the locus of the centers of all circles of a given radius a, in the same plane, passing through a fixed point, is [tex](x-s)^{2}[/tex] + [tex](y-b)^{2}[/tex] = [tex]a^{2}[/tex]
To learn more about the locus of the center:
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