Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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

Sagot :

theleangreenbean

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]

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.