Answer:
[tex](x+1)^2+(y+2)^2=25[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given:
- Center = (-1, -2)
- Point on the circle = (2, 2)
Substitute the given center and solution point into the formula and solve for r²:
[tex]\implies (2-(-1))^2+(2-(-2))^2=r^2[/tex]
[tex]\implies (2+1)^2+(2+2)^2=r^2[/tex]
[tex]\implies (3)^2+(4)^2=r^2[/tex]
[tex]\implies 9+16=r^2[/tex]
[tex]\implies 25=r^2[/tex]
Substitute the given center and found value of r² into the formula to create an equation of a circle with the given characteristics:
[tex]\boxed{(x+1)^2+(y+2)^2=25}[/tex]
