Question

2. Write the equation of a circle whose center is (-3,-1) and has the point (-4,-5) on its circumference.

Answer 1

We have that the equation of the circle with center (h,k) and radius r is:

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

in this case, we have that the center is (h,k) = (-3,-1), and the point (x,y) = (-4,-5) is on its circumference. Then, we can use these ordered pairs to find the value of r^2:

`\begin{gathered} (h,k)=(-3,-1) \\ (x,y)=(-4.-5) \\ \Rightarrow(-4-(-3))^2+(-5-(-1))^2=r^2 \\ \Rightarrow(-4+3)^2+(-5+1)^2=r^2 \\ \Rightarrow(-1)^2+(-4)^2=r^2 \\ \Rightarrow1+16=r^2 \\ \Rightarrow r^2=17 \end{gathered}`

therefore, the equation of a circle with center (-3,-1) and has the point (-4,-5) in its circumference is:

`(x+3)^2+(y+1)^2=17`