In RD Sharma Solutions for Class 12th Maths Chapter 16 tangents and normals, students study the topics related to tangents and normal in a deep manner. A tangent occurs only when there is a curve, so the tangent of a circle is described as a straight line that touches the circle at a single point. So, the point where the tangent touches the circle is called the point of contact or the point of tangency.
On the other hand, normal is a term used in geometry. It is an object such as a line, vector or ray that is considered perpendicular to a given object. To give an example, in two dimensions, the normal line to a curve at a given point is the line perpendicular to the tangent line of the curve at that point.
Another topic called the slope of a line is also being discussed. In maths, the slope is used to represent the steepness and direction of a particular line. Using two of the points on the line, one can simply identify the rise and the run. The vertical change between two points is called the rise, whereas the horizontal one is the run. The slope is nothing but the rise divided by the run.
Apart from that, students get to learn a topic called slopes of tangent and normal. The difference between the slope of normal and the slope of a tangent is that each normal line is perpendicular to the tangent line drawn when the normal meets the curve. So, it is seen that the slope of each normal line is described as the opposite or reciprocal of the slope of the corresponding tangent line, which a derivative can easily derive.
Students are taught how to find the slopes of the tangent and normal at a given point. Equations of tangent and normal are also taught. Finally, they are taught to find the point on a given curve at which the tangent is parallel or perpendicular to a given line.
They are also educated on finding the miscellaneous applications of tangents and normal, finding the equations of the curve, angle of intersection of two curves and orthogonal curves.