Question

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

• A. $4$
• B. $6$
• C. $10$
• D. $9$

Answer 1

The correct option is D $9$


Equation of tangent at $P(2,3)$ is $2y-x=4$

Required area
$=\frac{1}{2}(2\times 4)+\underset{0}{\overset{3}{\int }}\left(\right(y-2{)}^2+1)dy-\frac{1}{2}(1\times 2)$
$=3+{[\frac{(y-2{)}^3}{3}+y]}_0^3=3+6=9$