How do you find the normal to a curve at a given co-ordinate?
- You first find the gradient of the tangent to the curve at this given co-ordinate by differentiating the given equation of the curve, and then, assuming the equation of the curve is in terms of x, replacing the x in the result you got by differentiating with the x co-ordinate of the given co-ordinate. Calculating this will give you the gradient of the tangent, which we will call A. 2) As the gradient of the tangent is perpendicular to the gradient of the normal at any point, you then get the gradient of the normal by dividing -1 by the gradient of the tangent, A, and we will call the result B. 3) Then you use the standard form of a straight line, y= mx + c, where m is the gradient and c is the y-intercept. You replace x and y by the x and y co-ordinates in the given co-ordinate, and then replace m by the result you found just now, B. Solving for c will give you the y-intercept of the line, and then you can finally replace m with B and c by the result you just found, and you have the normal line to your curve.
