Given:
Center of a circle is (3,9).
Solution point is (-2,21).
To find:
The standard form of the circle.
Solution:
Radius is the distance between center (3,9) and the solution point (-2,21).
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]r=\sqrt{(-2-3)^2+(21-9)^2}[/tex]
[tex]r=\sqrt{(-5)^2+(12)^2}[/tex]
[tex]r=\sqrt{25+144}[/tex]
On further simplification, we get
[tex]r=\sqrt{169}[/tex]
[tex]r=13[/tex]
The radius of the circle is 13 units.
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where, (h,k) is the center and r is the radius.
Putting h=3, k=9 and r=13, we get
[tex](x-3)^2+(y-9)^2=(13)^2[/tex]
[tex](x-3)^2+(y-9)^2=169[/tex]
Therefore, the standard form of the circle is [tex](x-3)^2+(y-9)^2=169[/tex].
