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: 4x 2 + 9y 2 = 36 at (3 cos θ, 2 sin θ)

Philoid · Accepted Answer

finding the slope of the tangent by differentiating the curve

m(tangent) at (3 cos θ, 2 sin θ) =

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at (3 cos θ, 2 sin θ) =

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

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