The area of the region bounded by the parabola (y – 2)^2 = x – 1, the tangent to the parabola

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

  1. 3
  2. 6
  3. 9
  4. 12

Answer

Equation of tangent at (2, 3): x – 2y + 4 = 0

Required area: 0∫3 [(y - 2)2 + 1 - 2y + 4] dy

= 0∫3 [(y - 2)2 - 2y + 5] dy

= 0∫3 [(y2 - 6y + 9] dy

= [y3/3 - 3y2 + 9y]03

= [9 - 27 + 27] = 9

The correct option is C.