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

Question

Dr. Abubacker · Accepted Answer

(b)
The equation of tangent at (2,3) to the given parabola is
$x = 2y - 4$
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$	herefore$ Required area
$= \int_{0}^{3}{\{\left( y - 2)^{2} + 1 - 2y + 4 ight\} dy}$
$= \left\lbrack \frac{(y - 2)^{3}}{3} - y^{2} + 5y ightbrack_{0}^{3}$
$= \frac{1}{3} - 9 + 15 + \frac{8}{3}$
$= 9\ sq\ units$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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