IDNLearn.com: Where your questions are met with thoughtful and precise answers. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.
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]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.