The area of the region bounded by the parabola (y-2)^2=x-1 , the tangent to the parabola at the point (2,3) and the x -axis is

Step-by-step solution

Equation of tangent at (2,3) to aligned & (y-2)^2=x-1 is S₁=0 & x-2 y+4=0 aligned Required Area = Area of O C B+ Area of OAPD - Area of P C D aligned & = 1 2 (4 2)+ ₀^3 (y^2-4 y+5 ) d y- 1 2 (1 2) & =4+ [ y^3 3 -2 y^2+5 y ]₀^3-1=4-9-18+15-1 & =28-19=9 sq. units aligned (or) Area = ₀^3 (2 y-4-y^2+4 y-5 ) d y= ₀^3 (-y^2+6 y-5 ) d y=- ₀^3(3-y)^2 d y= [ (y-3)^3 3 ]₀^3= 27 3 =9 sq.units