Question

What is the standard form of the equation of a circle passing through Center at the point (-3, 1) and tangent to the y-axis?

Answer 1

`(x+3)^2+(y-1)^2=9`

Explanation:

I assume you meant "with center at `(-3,1)`"

The general form for a circle with center `(a,b)` and radius `r` is
`color(white)("XXX")(x-a)^2+(y-b)^2=r^2`

If the circle has its center at `(-3,1)` and is tangent to the Y-axis then it has a radius of `r=3`.

Substituting `(-3)` for `a`, `1` for `b`, and `3` for `r` in the general form gives:
`color(white)("XXX")(x-(-3))^2+(y-1)=3^2`
which simplifies to the Answer above.

graph{(x+3)^2+(y-1)^2=9 [-8.77, 3.716, -2.08, 4.16]}