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The triangle formed by the tangent to the curve f(x) = x 2 + bx - b at the point (1,1) and the coordinate axes, lies in the first quadrant. If its area is 2, then the value of b is a) -1 b) 3 c) -3 d) 1

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


 


a) -1          b) 3                   c)  -3               d) 1

Grade:Upto college level

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Raghu,

 

Eqn of tangent at (1,1) is

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

 

Points where it will intersect the co-ord axis is: (0,-b-1) and ([b+1]/[b+2],0) ------- {obtained by putting x=0 and y=0 in the tangent equation}

So 1/2*|-b-1|*|(b+1)/(b+2)| = 2 or (b+1)2/|b+2| = 4.

Clearly b=-3.

Option (C).

 

Regards,

Ashwin (IIT Madras).

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