If is the area of the triangle formed by the positive x -axis and the normal and tangent to the circle x^2+y^2=4 at (1, 3 ) , then is equal to

Step-by-step solution

Given equation of circle is x^2+y^2=4 On differentiating w.r.t. x , we get aligned & 2 x+2 y d y d x =0 & d y d x =- x y & ( d y d x )_ (1, 3 ) =- 1 3 & aligned Equation of tangent at (1, 3 ) is aligned & & y- 3 & =- 1 3 (x-1) & & 3 y-3 & =-x+1 & & x+ 3 y & =4 aligned and equation of normal at (1, 3 ) is array rlrl y- 3 & = 3 (x-1) & & 3 x-y & =0 array Intersection point of Eqs. (i) and (ii) is (1, 3 ) . Area of O A B aligned & = 1 2 O B A D= 1 2 4 3 & =2 3 aligned