VITEEE 2014 Paper

Given curve is y = f (x) = x2 + bx - b
⇒ f ' (x) = 2x + b
The equation of tangent at point (1, 1) is
y - 1 = (

dy

dx

)(1,1) (x - 1)
⇒ y - 1 = (b + 2) (x - 1)
⇒ (2 + b) x - y = 1 + b
⇒

x

( 1+b 2+b )

-

y

(1+b)

= 1

So, OA =

1+b

2+b

and OB = -(1 +b)
Now, area of Δ AOB =

1

2

×

(1+b)[−(1+b)]

(2+b)

= 2
⇒ 4 (2 + b) + (1+b)2 = 0
⇒ b2 + 6b + 9 = 0
⇒ (b+3)2 ⇒ b = - 3