1
A line passing through the point A(-2, 0) touches the parabola P: y2 = x - 2 at the point B in the first quadrant. The area of the region bounded by the line AB, parabola P and the x-axis, is :
- 3
- 73
- 83
- 2
Answer
(3) 83
Solution
Let B = (t2 + 2, t), t > 0.
Tangent at B: 2yt = x + (t2 + 2) - 4, i.e. 2ty = x + t2 - 2
It passes through A(-2, 0): 0 = -2 + t2 - 2 t2 = 4 t = 2
B(6, 2); line AB: 4y = x + 2, i.e. x = 4y - 2
[figure]
Required area (strips parallel to the x-axis, 0 y 2):
= 02 [(y2 + 2) - (4y - 2) ] dy = 02 (y - 2)2 dy
= [ (y - 2)33 ]02 = 0 - (- 83 ) = 83
Answer: (3)
JEE Main 2025 (Online) 4th April Evening Shift