Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

The triangle formed by the tangent to the curve f(x) = x2 + bx - b at the point (1, 1) and the co-ordinate axes, lies in the first quadrant. If its area is 2 then the value of b is

1) –1

2) 3

3) –3

4) 1

Solution:

Given f(x) = x2 + bx – b

Slope, m = dy/dx

= 2x + b

At (1,1)

m = 2 + b

The equation of the tangent at (1,1) is y-y1 = m(x-x1)

y – 1 = (2 + b)(x – 1)

y – 1 = (2 + b)x – (2 + b)

y – (b + 2)x = -2 – b + 1

y – (b + 2)x + b + 1 = 0

(2 + b)x – y = (b + 1)

x/(b + 1)/(2 + b) – y/(1 + b) = 1

OA = (b + 1)/(2 + b)

OB = -( 1 + b)

Area of triangle OAB = 1/2 (OA. OB)

½ (b + 1)/(2 + b)×-( 1 + b) = 2 (given area = 2)

(1 + b)2 + 4(2 + b) = 0

b2 + 6b + 9 = 0

(b + 3)2 = 0

So b = -3

Hence option (3) is the answer.

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