Question

Normal line to y = x2 – X – 1, with
a tangent point (2,1):​

Answer 1

Answer:

The given curve is y=x²+1 at (1,2).

The equation of tangent is y'-y'=m(x-x')

(x',y')=(1,2)

Differentiating y we get

y'=D(x²+1)=2x+0

y'=2x

m=2(1)=2

y-2=2(x-1)

y-2=2x-2

y=2x-2+2

y=2x

The equation of normal is y'-y'=(-1/m)(x-x')

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

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

2y-4=-x+1

2y=-x+1+4

2y+x=5