Find the equation of the tangent and the normal to the curves at the i

1.	Find the equation of the tangent and the normal to the curves at the indicated points: x = at2, y = 2at, at t = 1
Answer» Given as x = at², y = 2at, at t = 1 Differentiate with respect to t, to get slope of tangent dx/dt = 2at dy/dt = 2a Dividing dy/dt and dx/dt to obtain the slope of tangent dy/dx = 1/t m(tangent) at t = 1 is 1 The normal is perpendicular to tangent therefore, m₁m₂ = – 1 m(normal) at t = 1 is -1 The equation of tangent is given by y – y₁ = m(tangent)(x – x₁) y - 2a = 1(x - a) The equation of normal is given by y – y₁ = m(normal)(x – x₁) y - 2a = -1(x - a)

Find the equation of the tangent and the normal to the curves at the indicated points: x = at2, y = 2at, at t = 1

Answer»

Given as x = at², y = 2at, at t = 1

Differentiate with respect to t, to get slope of tangent

dx/dt = 2at

dy/dt = 2a

Dividing dy/dt and dx/dt to obtain the slope of tangent

dy/dx = 1/t

m(tangent) at t = 1 is 1

The normal is perpendicular to tangent therefore, m₁m₂ = – 1

m(normal) at t = 1 is -1

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

y - 2a = 1(x - a)

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

y - 2a = -1(x - a)