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. $6$
• B. $3$
• C. $12$
• D. $9$

Answer 1

The correct option is D $9$

Equation of tangent at $(2,3):x-2y+4=0$

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

$={\int }_0^3[y^2-6y+9]dy={[\frac{y^3}{3}-3y^2+9y]}_0^3$

$=[9-27+27]=9$