A point P lying inside the curve y = 2 a x − x 2 is moving such that its shortest distance from the curve at any position is greater than its distance from x-axis. The point P enclose a region whose

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A point P lying inside the curve y = 2 a x − x 2 ​ is moving such that its shortest distance from the curve at any position is greater than its distance from x-axis. The point P enclose a region whose area is equal to

TestHub · Accepted Answer

y = 2 a x − x 2 ​ ⇒ ( x − a ) 2 + y 2 = a 2 . Let P ( h , k ) be a point, then BP > PN . For the boundary condition BP = PN = k . Now A P = a − k = ( h − a ) 2 + k 2 ​ ⇒ k = h − 2 a h 2 ​ . ∴ boundary of the region is y = x − 2 a x 2 ​ . Required area = 2 ∫ 0 a ​ ( x − 2 a x 2 ​ ) d x = 3 2 a 2 ​ .

Mathematics - Area Under Curves Question with Solution | TestHub

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