A common tangent equation is a mathematical equation that represents the tangent line that touches two given curves at the same point. It is used to find the point of intersection between the two curves.
To find the common tangent equation, you need to first find the slopes of the two curves at the point of intersection. Then, use the formula y-y1=m(x-x1) where m is the slope and (x1, y1) is the point of intersection to write the equation in point-slope form. Finally, simplify the equation to get the common tangent equation.
Yes, there can be more than one common tangent between two curves. This can happen when the two curves are parallel to each other or when they have multiple points of intersection.
Common tangent equations have various applications in real life, especially in the fields of physics and engineering. They are used to determine the point of contact between two objects, such as a ball rolling on a surface, or in designing curved structures like bridges and roller coasters.
Yes, common tangent equations can be used for non-linear curves. However, the process of finding the equation may be more complex as it involves taking the derivatives of the curves to find their slopes.