Answer:
[tex](x-6)^2+(y-4)^2=25[/tex]
Step-by-step explanation:
It is given that,
Center of the circle = (6,4)
Circle passes through the point = (2,1)
Radius of the circle is distance between center (6,4) and point on he circle (2,1).
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]r=\sqrt{(2-6)^2+(1-4)^2}[/tex]
[tex]r=\sqrt{(-4)^2+(-3)^2}[/tex]
[tex]r=\sqrt{16+9}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r=5[/tex]
Standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, r is radius and (h,k) is center.
Substitute h=6, k=4 and r=5 in the above equation.
[tex](x-6)^2+(y-4)^2=5^2[/tex]
[tex](x-6)^2+(y-4)^2=25[/tex]
Therefore, the equation of circle is [tex](x-6)^2+(y-4)^2=25[/tex].
