Answer: The required equation of the circle is [tex]x^2+y^2+2x+8y+13=0[/tex]
Step-by-step explanation: We are given to find the equation of the circle with center (-1, -4) and radius of length 2 units.
We know that
the STANDARD equation of a circle with center at the point (h, k) and radius of length r units is given by
[tex](x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
For the given circle,
center, (h, k) = (-1, -4) and radius, r = 2 units.
So, from equation (i), we get
[tex](x-(-1))^2+(y-(-4))^2=2^4\\\\\Rightarrow (x+1)^2+(y+4)^2=4\\\\\Rightarrow x^2+2x+1+y^2+8y+16=4\\\\\Rightarrow x^2+2x+y^2+8y+17-4=0\\\\\Rightarrow x^2+y^2+2x+8y+13=0[/tex]
Thus, the required equation of the circle is [tex]x^2+y^2+2x+8y+13=0[/tex]
