Question

write an equation of s circle with a radius of a circle with an equation of (x- 6)² + (y + 3)² =r² and containing (4, 1)

Answer 1

We have the circle equation

$(x-6)^2+(y+3)^2=r^2$

We will find the radius r by substituting the given point, which belongs to the circle, that is,

$(4-6)^2+(1+3)^2=r^2$

which gives

$\begin{gathered} (-2)^2+4^2=r^2 \\ 4+16=r^2 \\ 20=r^2 \end{gathered}$

Then, the circle equation is

$(x-6)^2+(y+3)^2=20$