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Determine the equation of the circle with center (-7,7)(−7,7) containing the point (-2,-5)(−2,−5)

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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:

  1. Plug the center into the general equation as (h,k)
  2. Plug the given point into the general equation as (x,y)
  3. Solve for r²
  4. 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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