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 = at 2 , y = 2at at t = 1.

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 = 1 is 1

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at t = 1 is – 1

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

y – 2a = 1(x – a)

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

y – 2a = – 1(x – a)