Tangents and Normals

Note 1:

If m = 0 the tangent is parallel to x-axis.

Note 3:

Equation of the tangent at (x₁,y₁) is

or

Note 4:

Equation of the normal at (x₁,y₁) is

or

Example:

Find the equation of the tangent to the curve which is parallel to the line 4x - 2y + 5 = 0.

Solution:

Since the tangent to the given curve is parallel to the line

4x - 2y + 5 = 0

Slope of the tangent = Slope of the given line

On simplification, the equation is 48 x - 24y = 23.