# X-intercepts and Y-intercepts

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.

In this picture, the graph crosses the x-axis at the ordered pair .  Since every ordered pair on the x-axis has a y coordinate of zero we can let to find x-intercepts.

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

In this picture, the graph crosses the y-axis at the ordered pair .  Since every ordered pair on the y-axis has a x coordinate of zero we can let to find y-intercepts.

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

# Finding the Intercepts of a Circle Touching an Axis (Tangent to an axis)

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).

# Finding the Intercepts of a Circle (4 Intercepts)

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.

Approximately and

This equation has two x-intercepts. and

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

Approximately and

This equation has two y-intercepts. and