Find the equation of the tangent and the normal to the following curves at the indicated points:

Question

Find the equation of the tangent and the normal to the following curves at the indicated points: x = a sec t, y = b tan t at t.

Philoid · Accepted Answer

finding slope of the tangent by differentiating x and y with respect to t

Now dividing and to obtain the slope of tangent

m(tangent) at t =

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at t =

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

equation of normal is given by y – y₁ = m(normal)(x – x₁)