question_answer

The area of the region bounded by the parabola\[{{(y2)}^{2}}=x1,\]the tangent to the parabola at the point (2, 3) and the x-axis is

A) 3

B)                        6                             

C)        9                             

D)        12

Correct Answer: C

Solution :

Equation of tangent at (2, 3) \[\equiv x2y+4=0\] Required area \[=\int\limits_{0}^{3}{\left[ {{(y-2)}^{2}}+1-2y+4 \right]}\,dy\] \[=\int\limits_{0}^{3}{\left[ {{(y-2)}^{2}}-2y+5 \right]}\,dy\] \[=9\text{ }sq.\text{ }units\]