# How do you write the equation of a circle given center (3,-7) and tangent to the y-axis?

##### 3 Answers

#### Explanation:

The equation for a circle is

Plugging in

Since you want the circle to be tangent to the

A radius of 3, since the

Here's the graph:

Using the general equation of a circle, set up the translations accordingly, then with a point on the

#### Explanation:

The equation of a circle in the center is

The center can be translated by subtracting from the

**If it had a radius of #1#** (although we don't know what it is yet), this is what it looks like:

Now, as for the radius, and the circle being tangent to the y-axis. This means it has to touch the *one* point on the circle that is on the

Thinking about the center of the circle, and perhaps the figure above, as we expand the radius, the first point that touches the

Why don't we plug that into the equation we already have, and solve for

And simplify:

That makes sense algebraically, but since this is a geometric figure, radii are positive:

Plugging that back in to our equation:

And here's what it looks like:

Indeed, the center is at

#### Explanation:

The reqd. circle **touches** the **Axis.**

From **Geometry,** we know that, the **distance** from

**Centre** to the **tangent** line equals **radius**

Now, the **distance** from **Axis,** is

Hence, the eqn. follows :