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

3

6

9

12

Solution

Equation of tangent at (2, 3)

≡ x – 2y + 4 = 0
Required Area
$space equals space integral subscript 0 superscript 3 space left square bracket space left parenthesis straight y minus 2 right parenthesis squared space plus space 1 minus 2 straight y plus 4 right square bracket space dy space equals space integral subscript 0 superscript 3 space left square bracket space left parenthesis straight y minus 2 right parenthesis squared space minus space 2 straight y space plus 5 right square bracket space dy space equals 9 space sq. space units$