Question

How do you write an equation for a circle with center (2,-6); tangent to the y-axis?

Answer 1

The equation is: `(x-2)^2+(y+6)^2=4`

Explanation:

The equation of a circle with center `(h,k)` and radius `r` is:

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

We know the center is `(2,-6)`.

Since the circle is tangent to the y-axis, we know that the distance from the center to the y-axis is 2 units, so the radius is 2.

The equation is: `(x-2)^2+(y+6)^2=4`

Here's a figure:
graph{(x-2)^2+(y+6)^2=4 [-9.13, 10.87, -9.36, 0.64]}