Before attempting this revision your must have knowledge of what tangents are. How to find gradients of tangents and be able to form general formulas for tangents. This is just an expansion from Gradient of a Tangent to a curve and without any knowledge of tangents be ready for huge headaches. You know that a tangent to a curve is a straight line which touches the curve at a certain point. Well… The normal to a curve is the straight line perpendicular to the tangent at the same point as the tangent attachment to the curve. In the following illustration the normal to the curve is the blue line while the orange line is the tangent and the red line the curve. If the gradient of the tangent is m …then the gradient of the normal is -1/m For instance; if the gradient of a tangent is 4 then the gradient of the normal is -1/4 It is as simple as that, this is how you find the normal to the curve at a certain point but you first need to differentiate to find the gradient first. In most cases when working with tangents and normals there will be a need to find the equations of the tangents and normals at a certain point. In the following examples we shall be exploring just that. To find the equations of either the tangent of the normal we need to know the gradient of the curve and the point of the line then we use the following equation; where m is the gradient and (x1, y1) is the point given.