Given:
The center of the circle = (-2,5)
The radius of the circle = [tex]3\sqrt{2}[/tex] units.
To find:
The equation of the circle is standard form.
Solution:
The standard form of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
Where, (h,k) is the center of the circle and r is the radius of the circle.
It is given that the center of the circle is (-2,5). So, [tex]h=-2,\ k=5[/tex].
The radius of the circle is [tex]3\sqrt{2}[/tex] units. So, [tex]r=3\sqrt{2}[/tex].
Putting [tex]h=-2,\ k=5[/tex] and [tex]r=3\sqrt{2}[/tex] in (i), we get
[tex](x-(-2))^2+(y-(5))^2=(3\sqrt{2})^2[/tex]
[tex](x+2)^2+(y-5)^2=18[/tex]
Therefore, the equation of the circle is [tex](x+2)^2+(y-5)^2=18[/tex].
