Equation of a normal to a curve
You must have a general understanding of graph gradients, tangents, normals and derivatives. This would probably be a reminder rather than a lesson. You must know that a normal is perpendicular to the tangent. Which means the gradient of a normal is 1 divide by the gradient of the tangent. To find an equation of a normal to a curve use the following steps.
- Find the derivative f ’(x) of the given function, this will be merely the equation of the gradient for that function.
- Substitute in the x-coordinates of the given point in the derivative to find the gradient at this point.
- The gradient of the normal is; m = 1/(dy/dx) which is the gradient you need to use in the following formula.
Place the found values in the following formula. You will need the m which is the gradient, x-coordinate which is the given value and the y-coordinate, you find this by substituting it in the original function.
You might be required or for your purpose to write the equation of the normal in this form;