FIND THE EQUATION OF TANGNET AND NORMAL TO THE CURVE WORKSHEET

Find the tangent and normal of the following curves at the given points on the curve :

Problem 1 :

y = x² - x⁴at (1, 0)

Problem 2 :

y = x⁴ + 2e^x at (0, 2)

Problem 3 :

y = x sin x at (π/2, π/2)

Problem 4 :

x = cos t, y = 2 sin² t at t = π/3

Problem 5 :

Find the equations of the tangents to the curve

y = (x + 1) / (x - 1)

which are parallel to the line x + 2y = 6.

Answer Key

Equation of tangent

1) 2x + y = 2

2) 2x - y = - 2

3) y = x

4) 4x + 2y -5 = 0

x + 2y - 7 = 0 and

x + 2y = -1

Equation of normal

x - 2y = 1

x + 2y = 4

y = -x + π

x - 4y + 5 = 0