Tangent Line to a Circle

An equation of the form describes a line tangent to the circle at the point . Drag the sliders for and to see how the graph and equation change. You can show or hide the circle that the line is tangent to as well as the radius to the point of tangency. To see where this equation comes from, show the "Point on the Line." Be sure to have the radius showing as well. Notice the radius and the segment to the point form a right triangle, which leads to the relationship: Multiplying both sides by , we get: