Let 'c' be the constant number such that c 1 . If the least area of the figure given by the line passing through the point (1, c) with gradient ' m ' and the parabola y = x 2 is

Question

Let 'c' be the constant number such that c > 1 . If the least area of the figure given by the line passing through the point (1, c) with gradient ' m ' and the parabola y = x 2 is 36 sq. units find the value of ( c 2 + m 2 ) .

TestHub · Accepted Answer

Use the intersection discriminant D and the parabolic-segment area A: y = m x + c − m , x 2 = m x + c − m , D = ( m − 2 ) 2 + 4 ( c − 1 ) . A = D 3/2 /6. A m i n ​ = [ 4 ( c − 1 ) ] 3/2 /6 = 36 ⇒ c = 10 , m = 2. c 2 + m 2 = 104. ​

Mathematics - Area Under Curves Question with Solution | TestHub

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