Answer:
The equation of circle is [tex](x+8)^2+(y+9)^2=9[/tex].
Step-by-step explanation:
It is given that the diameter of circle is 6 units and the center of circle is (-8,-9).
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where, (h,k) is center of the circle and r is radius.
The diameter of circle is twice of its radius
[tex]d=2r[/tex]
[tex]6=2r[/tex]
[tex]r=3[/tex]
The radius of the circle is 3 and the center of circle is (-8,-9). So, the required equation of circle is
[tex](x-(-8))^2+(y-(-9))^2=3^2[/tex]
[tex](x+8)^2+(y+9)^2=9[/tex]
Therefore the equation of circle is [tex](x+8)^2+(y+9)^2=9[/tex].
