Question

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

A
3
B
6
C
9
D
12

Solution

## The correct option is C $$9$$Equation of tangent at $$(2,3)$$ $$:$$   $$2y=x+4$$$$\displaystyle \int_{0}^{3}[(y-2)^{2}+1]-[2y-4] \text{ }dy$$$$=\displaystyle \int_{0}^{3}[(y-2)^{2}-2y+5]\text{ }dy$$$$=\left[\dfrac{(y-2)^{3}}{3}-y^{2}+5y\right]_{0}^{3}$$$$=9$$Mathematics

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