Question

Area bounded by the parabola (y − 2)² = x − 1, the tangent to it at the point P(2, 3) and the x-axis is equal to

• A. 9 sq. units
• B. 6 sq. units
• C. 3 sq. units
• D. None of these

Answer 1

Answer: (A)

9 sq. units

Answer 2

(y – 2)² = (x – 1) ⇒ 2(y – 2). = 1

⇒$\frac { d y } { d x } = \frac { 1 } { 2 ( y - 2 ) }$

Thus equation of tangent at P(2, 3) is,

(y − 3) = $\frac { 1 } { 2 }$(x − 2) i.e. x = 2y - 4.

Required area $\Delta = \int _ { 0 } ^ { 3 } \left( ( y - 2 ) ^ { 2 } + 1 - ( 2 y - 4 ) \right) d y$

$= \left( \frac { ( y - 2 ) ^ { 3 } } { 3 } - y ^ { 2 } + 5 y \right) _ { 0 } ^ { 3 }$ = 9 sq. units.