Question

Find the area of the region enclosed by the parabola y^2 = 16x and the
chord BC where B(1,4) and C(9,12).​

Answer 1

Given : parabola y^2 = 16x the chord BC where B(1,4) and C(9,12).​

To Find :  area of the region enclosed

Solution:

y² = 16x  => y = 4√x

B(1,4) and C(9,12).​

slope  = ( 12 - 4)/(9 - 1) = 8/8 = 1

y - 4 = 1 (x - 1)

=> y = x  + 3

Area of region enclosed

$\int\limits^9_1 {(4\sqrt{x} -(x+3))} \, dx$

=   [8 x√x /3  - x²/2  - 3x ]$]_1^9$

= 8 * 9 * 3 / 3  - 81/2 - 27  - ( 8/3 - 1/2  - 3)

= 72  - 135/2  - (16 - 3 - 18)/6

= 9/2  +5/6

= ( 27+5)/6

= 32/6

= 16/3

= 5.33 sq units

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