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: y = x2 at (0, 0)
Answer» Given as y = x² at (0, 0) Differentiate the given curve, to get the slope of the tangent dy/dx = 2x m (tangent) at (x = 0) = 0 Normal is perpendicular to tangent so, m₁m₂ = – 1 n(normal) at (x = 0) = 1/10 As we can see that the slope of normal is not defined The equation of tangent is given by y – y₁ = m(tangent)(x – x₁) y = 0 The equation of normal is given by y – y₁ = m(normal)(x – x₁) x = 0

Find the equation of the tangent and the normal to the curves at the indicated points: y = x2 at (0, 0)

Answer»

Given as y = x² at (0, 0)

Differentiate the given curve, to get the slope of the tangent

dy/dx = 2x

m (tangent) at (x = 0) = 0

Normal is perpendicular to tangent so, m₁m₂ = – 1

n(normal) at (x = 0) = 1/10

As we can see that the slope of normal is not defined

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

y = 0

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

x = 0