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The area of the region bounded between the line x=9 and the parabola y2=16x is
- a)144 sq units
- b)27 sq units
- c)104 sq units
- d)54 sq units
Correct answer is option 'A'. Can you explain this answer?
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The area of the region bounded between the line x=9 and the parabola y...
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The area of the region bounded between the line x=9 and the parabola y...
Solution:
Given, the line x=9 and the parabola y^2=16x.
Let us plot the given line and parabola on a graph.
As shown in the graph, we can observe that the line x=9 intersects the parabola y^2=16x at two points A and B.
Now, we need to find the area of the region bounded between the line x=9 and the parabola y^2=16x.
Let the coordinates of point A be (a, b) and the coordinates of point B be (a, -b).
Then, we have a=9 and b=6.
Therefore, the area of the region bounded between the line x=9 and the parabola y^2=16x is given by:
∫(from -b to b) (x-9)dx
= [(x^2/2)-9x] (from -b to b)
= [(b^2/2)-9b]-[(-b^2/2)+9b]
= (b^2+18b)-(b^2-18b)
= 36b
= 36(6)
= 216 sq units
Hence, the correct option is A.
Given, the line x=9 and the parabola y^2=16x.
Let us plot the given line and parabola on a graph.
As shown in the graph, we can observe that the line x=9 intersects the parabola y^2=16x at two points A and B.
Now, we need to find the area of the region bounded between the line x=9 and the parabola y^2=16x.
Let the coordinates of point A be (a, b) and the coordinates of point B be (a, -b).
Then, we have a=9 and b=6.
Therefore, the area of the region bounded between the line x=9 and the parabola y^2=16x is given by:
∫(from -b to b) (x-9)dx
= [(x^2/2)-9x] (from -b to b)
= [(b^2/2)-9b]-[(-b^2/2)+9b]
= (b^2+18b)-(b^2-18b)
= 36b
= 36(6)
= 216 sq units
Hence, the correct option is A.
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The area of the region bounded between the line x=9 and the parabola y2=16x isa)144 sq unitsb)27 sq unitsc)104 sq unitsd)54 sq unitsCorrect answer is option 'A'. Can you explain this answer?
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