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17/01/2022 3:00 pm
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The area of the region bounded by the parabola (y – 2)2 = (x – 1), the tangent to it at the point whose ordinate is 3 and the x-axis is
(1) 9
(2) 10
(3) 4
(4) 6
1 Answer
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17/01/2022 3:05 pm
Correct answer: (1) 9
Explanation:
y = 3 ⇒ x = 2
Point is (2, 3)
Diff. w.r.t x2 (y – 2) y' = 1
⇒ y' = \(\frac{1}{2(y-2)}\)
⇒ y'(2, 3) = \(\frac{1}{2}\)
⇒ \(\frac{y-3}{x-2}\) = \(\frac{1}{2}\)
⇒ x - 2y + 4 = 0
Area = \(\int_0^3\)((y - 2)2 + 1 - (2y - 4)) dy
= 9 sq. units