The equation of a circle with center at [tex](8, 10)[/tex] and radius [tex]6[/tex] will be
[tex](x-8)^2+(y-10)^2=36[/tex] which is given in option [tex](3)[/tex] .
What is equation of a circle ?
Equation of a circle is written in the form [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.
We have,
The center at [tex](8, 10)[/tex] and radius is [tex]6[/tex] .
i.e.
[tex]h=8[/tex]
[tex]k=10[/tex]
[tex]r=6[/tex]
So, using the above given equation,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Putting the above values in this equation
We get,
[tex](x-8)^2+(y-10)^2=(6)^2[/tex]
i.e.
[tex](x-8)^2+(y-10)^2=36[/tex]
This is the equation of a circle which is derived using the above given equation.
Hence, we can say that the equation of a circle with center at [tex](8, 10)[/tex] and radius [tex]6[/tex] will be [tex](x-8)^2+(y-10)^2=36[/tex] which is given in option [tex](3)[/tex] .
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