At any given value of X, the value of the circles derivative equation will be equal to the slope of the tangent line at that given point. Drag the tangent line around the circle to observe this.
Sample Problem: Start by finding a point on either circle. For example, on the green circle the point (7.7945956 , 3.7354745). Also record the slope of the tangent at that point (In this case; -0.85114262). Plug the X & Y values of the point into the derivative of the circle equation. Observe that the answer is the same as the slope of the tangent.
| Green Circle Point | |||
| Orange Circle Point | |||
| Slope of Tangent to Orange Circle | |||
| Slope of Tangent to Green Circle | |||