Q21 of 26 Page 1

Using integration find the area of the triangle formed by positive x-axis and tangent and normal to the circle x2 + y2 = 4 at (1, √3).

OR


Evaluate as a limit of a sum.

Given that, equation of the circle is x2 + y2 = 4.


The equation of the normal to the circle at (1, √3) is the equation of the line joining the points (1, √3) and (0,0).



⇒ y = √3 x (i)


∴ equation of normal is y = √3 x.


Now, the equation of the tangent to the circle at (1, √3) is



⇒ √3 y – 3 = -x +1


(ii)


Putting y=0 , we get x=4


Hence, Δ AOB is formed by the positive x-axis and tangent and normal.



Now, Area of Δ AOB = Area of Δ AOC + Area of Δ ACB









= 2√3 sq. units


Hence, area of the triangle formed is 2√3 sq. units


OR


We have,


Where


Here, a =1 ,b=3 and f(x) = e2-3x+x2+1


∴ ⇒ hn=2


Now,












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