Question
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
BITSAT
Mathematics
Area Under Curves
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 3
- B. 6
- C. 9
- D. 12
Answer
C. 9
Step-by-step solution
The equation of the parabola is y^2-4 y-x+5=0 The equation of tangent at (2,3) is aligned 3 y-2(y+3)- x+2 2 +5 & =0 \\ 2 y-x-4 & =0 aligned Required area A is given by aligned & A= _0^3 (x_2-x_1 ) d y \\ & A= _0^3 [ \ (y-2)^2+1 \ -\ 2 y-4\ ] d y \\ & A= _0^3 (y^2-6 y+9 ) d y= _0^3(3-y)^2 d y \\ & =- [ (3-y)^3 3 ]_0^3=9 \\ & aligned
Related: Mathematics — Area Under Curves · All PYQ Banks