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).
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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
= [8 x√x /3 - x²/2 - 3x ]
= 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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