Question

How do you find general form of circle centered at (1,0) and containing point (-2,3)?

Answer 1

`(x-1)^2+y^2=18`

Explanation:

The general form of a circle:

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

where `(h,k)` is the center of the circle and `r` is the radius.

Since the center of the circle is `(1,0)`, we can fill in `h` and `k`.

`(x-1)^2+(y-0)^2=r^2`

Now, all we need to know is the radius length, which we can find by applying to distance formula with the circle's center and another point on the circle: `(-2,3)`.

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

`d=sqrt((-2-1)^2+(3-0)^2)`

`d=sqrt18`

Thus, the radius is `sqrt18`, and the radius is represented in the general form of a circle by `r^2`, so `r^2=18`.

Thus, the equation of the circle is:

`(x-1)^2+y^2=18`

graph{(x-1)^2+y^2=18 [-10, 10, -5, 5]}