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Sagot :
Equation of a Circle
Circular equations are often organized in the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
- [tex](h,k)[/tex] is where the circle is centered
- [tex]r[/tex] is the radius
To find the equation of a circle given its center and a point:
- Plug the center into the general equation as (h,k)
- Plug the given point into the general equation as (x,y)
- Solve for r²
- Plug (h,k) and r back into the original equation
Solving the Question
We're given:
- Center: (-7,7)
- Point: (-2,-5)
Plug the center into the general equation:
[tex](x-(-7))^2+(y-7)^2=r^2\\(x+7)^2+(y-7)^2=r^2[/tex]
Plug in the given point (-2,-5) and find r²:
[tex]((-2)+7)^2+((-5)-7)^2=r^2\\(5)^2+(-12)^2=r^2\\25+144=r^2\\r^2=169[/tex]
Plug the center and radius back into the original equation:
[tex](x-h)^2+(y-k)^2=169\\(x+7)^2+(y-7)^2=169[/tex]
Answer
[tex](x+7)^2+(y-7)^2=169[/tex]
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