# Line Equations : Tangents & Normals

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I) Find the equation of the tangent to y=x(1-x) at x=1

ii) Find the equation of the normal to y=x(1-x) at x=1

iii) Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)

https://brainmass.com/math/calculus-and-analysis/line-equations-tangents-normals-16505

#### Solution Preview

i.)

At x =1: y = 1*(1-1) = 0

Hence, given point (x1, y1)= (1,0)

dy/dx = y' = 1 - 2x

y'|(at x = 1) = 1 - 2*1 = -1

Hence, Eqn of tangent:

y -y1 = y'(x-x1)

=> y - 0 = (-1)*(x-1)

=> x + y = 1 --Answer

ii.)

Eqn of normal:

(x-x1) + y'(y-y1) = 0

=> (x-1) + (-1)*(y-0) = 0

=> x-1 -y = 0

=> x - y = 1 ...

#### Solution Summary

Tangents and normals are calculated.

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