Find the equation of the tangent and the normal to the following curves at the indicated points:
x = a (θ + sin θ), y = a (1 – cos θ) at θ

Question

Find the equation of the tangent and the normal to the following curves at the indicated points:x = a (θ + sin θ), y = a (1 – cos θ) at θ

Philoid · Accepted Answer

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

Now dividing and to obtain the slope of tangent

m(tangent) at theta is

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at theta is

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

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