Question

Write the standard form of the equation of the circle with the given characteristics. center: (-1, -2); solution point: (2, 2)

Part 2 ll
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Answer 1

`(x+1)^2+(y+2)^2=25`

Explanation:

`\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}}`

Given:

• Center = (-1, -2)
• Point on the circle = (2, 2)

Substitute the given center and solution point into the formula and solve for r²:

`\implies (2-(-1))^2+(2-(-2))^2=r^2`

`\implies (2+1)^2+(2+2)^2=r^2`

`\implies (3)^2+(4)^2=r^2`

`\implies 9+16=r^2`

`\implies 25=r^2`

Substitute the given center and found value of r² into the formula to create an equation of a circle with the given characteristics:

`\boxed{(x+1)^2+(y+2)^2=25}`