Question

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

• A. $3$
• B. $6$
• C. $9$
• D. $12$

Answer 1

The correct option is C $9$

Equation of tangent at $(2,3)$ $:$ $2y=x+4$

${\int }_0^3\left[\right(y-2{)}^2+1]-[2y-4]dy$

$={\int }_0^3\left[\right(y-2{)}^2-2y+5]dy$

$={[\frac{(y-2{)}^3}{3}-y^2+5y]}_0^3$

$=9$