Question

How do you find the equation of a circle passes through the origin and has its center at (-1,-9)?

Answer 1

`(x+1)^2+(y+9)^2=82`

Explanation:

If a circle has a center at `(x_c,y_c)=(-1,-9)` and passes through the origin (i.e. `(0,0)` )
then it has a radius of r=`sqrt((-1-0)^2+(-9-0)^2)=sqrt(82)`

the general formula for a circle with center `(x_c,y_c)` and radius `r` is
`color(white)("XXX")(x-x_c)^2+(y-y_c)^2=r^2`

So in this particular case:
`color(white)("XXX")(x-(-1))^2+(y-(-9))^2=82`
or
`color(white)("XXX")(x+1)^2+(y+9)^2=82`

graph{(x+1)^2+(y+9)^2=82 [-24.15, 21.45, -21.76, 1.06]}