Find the equation of the tangent and the normal to the following curves at the indicated points: x = 3 cos θ – cos 3 θ, y = 3 sin θ – sin 3 θ

Question

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)