An **x-intercept** is where the graph touches or crosses the x-axis.

A **y-intercept** is where the graph touches of crosses the y-axis.

**To find an x-intercept: **Let y=0 and solve for x.

**To find an y-intercept: **Let x=0 and solve for y.

**Example: **Find the intercepts of the circle for the given equation.

Solution:

To find an x-intercept, let y=0 and solve for x.

This equation has one x-intercept.

To find a y-intercept, let x=0 and solve for y.

Approximately and

This equation has two y-intercepts. and

A** tangent line to a circle** may be defined as a line that intersects the circle in a single point.

This circle is **tangent to the x-axis **since it is touching the x-axis in a single point. The x-axis (y=0) is the tangent line for the point on the circle (1,0).

**Example: **Find the intercepts of the circle for the given equation.

Solution:

To find an x-intercept, let y=0 and solve for x.

Approximately and

This equation has two x-intercepts. and

To find a y-intercept, let x=0 and solve for y.

This equation has one y-intercept. .

This circle is **tangent to the y-axis **since it is touching the y-axis in a single point. The y-axis (x=0) is the tangent line for the point on the circle (0,1).