Question

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

Answer 1

Equation of a Circle

Circular equations are often organized in the following form:

`(x-h)^2+(y-k)^2=r^2`

• 
  `(h,k)` is where the circle is centered
• 
  `r` 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:

`(x-(-7))^2+(y-7)^2=r^2\\(x+7)^2+(y-7)^2=r^2`

Plug in the given point (-2,-5) and find r²:

`((-2)+7)^2+((-5)-7)^2=r^2\\(5)^2+(-12)^2=r^2\\25+144=r^2\\r^2=169`

Plug the center and radius back into the original equation:

`(x-h)^2+(y-k)^2=169\\(x+7)^2+(y-7)^2=169`

Answer

`(x+7)^2+(y-7)^2=169`