Answer: The required equation of the circle is [tex] x^2+y^2+2x-4y=4.[/tex]
Step-by-step explanation: We are given to find the equation of a circle with center at the point (-1, 2) and a radius of 3 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, we have
center , (h, k) = (-1, 2) and radius, r = 3 units.
Therefore, from equation (i), we get
[tex](x-(-1))^2+(y-2)^2=3^2\\\\\Rightarrow (x+1)^2+(y-2)^2=9\\\\\Rightarrow x^2+2x+1+y^2-4y+4=9\\\\\Rightarrow x^2+y^2+2x-4y=4.[/tex]
Thus, the required equation of the circle is [tex] x^2+y^2+2x-4y=4.[/tex]
